Prime Factors, HCF & LCM (AQA GCSE Maths)

Exam Questions

3 hours54 questions
1
Sme Calculator
3 marks

Write 525 as a product of its prime factors.

Did this page help you?

2
Sme Calculator
2 marks

Express 56 as the product of its prime factors.

Did this page help you?

3
Sme Calculator
2 marks

Write 36 as a product of its prime factors.

Did this page help you?

4
Sme Calculator
3 marks

Trams leave Piccadilly

to Eccles every 9 minutes
to Didsbury every 12 minutes

A tram to Eccles and a tram to Didsbury both leave Piccadilly at 9 am.

At what time will a tram to Eccles and a tram to Didsbury next leave Piccadilly at the same time?

Did this page help you?

5
Sme Calculator
3 marks

Write 200 as a product of prime factors.
Give your answer in index form.

Did this page help you?

6
Sme Calculator
1 mark

Circle the lowest common multiple (LCM) of 5, 15 and 25

5 45 75 150

Did this page help you?

7
Sme Calculator
1 mark

Work out the lowest common multiple (LCM) of 20, 30 and 40

Circle your answer.

10 120 240 24 000

Did this page help you?

8
Sme Calculator
3 marks

Write 36 as a product of prime factors.
Give your answer in index form.

Did this page help you?

9
Sme Calculator
2 marks

Write 75 as a product of its prime factors.

Did this page help you?

10
Sme Calculator
3 marks

Write 504 as the product of its prime factors.

Did this page help you?

11
Sme Calculator
3 marks

You are given that 177147 equals 3 to the power of 11

Write 177 147 000 000 as a product of its prime factors.

Did this page help you?

12
Sme Calculator
3 marks

Carla runs every 3 days.
She swims every Thursday.
On Thursday 9 November, Carla both runs and swims.

What will be the next date on which she both runs and swims?

Did this page help you?

13
Sme Calculator
3 marks

Write 600 as a product of powers of its prime factors.
Show your working clearly.

Did this page help you?

14
Sme Calculator
2 marks

A2 to the power of n space cross times space 3 space cross times space 5 to the power of m

Write 8 A as a product of powers of its prime factors.

Did this page help you?

15a
Sme Calculator
3 marks

Write 720 as a product of its prime factors.
Show your working clearly.

15b
Sme Calculator
1 mark

Find the smallest whole number that 720 can be multiplied by to give a square number.

Did this page help you?

16
Sme Calculator
3 marks

Write 3.6 space cross times space 10 cubed as a product of powers of its prime factors.

Show your working clearly.

Did this page help you?

17
Sme Calculator
2 marks

Write 800 as a product of its prime factors.
Show your working clearly.

Did this page help you?

18
Sme Calculator
3 marks

Write space 880 spaceas a product of powers of its prime factors.
Show your working clearly.

Did this page help you?

19
Sme Calculator
2 marks

Find the Highest Common Factor (HCF) of 140 and 245.

Did this page help you?

1
Sme Calculator
3 marks

Buses to Acton leave a bus station every 24 minutes.
Buses to Barton leave the same bus station every 20 minutes.

A bus to Acton and a bus to Barton both leave the bus station at 9.00 am.

When will a bus to Acton and a bus to Barton next leave the bus station at the same time?

Did this page help you?

2
Sme Calculator
4 marks

Rita is going to make some cheeseburgers for a party.
She buys some packets of cheese slices and some boxes of burgers.

There are 20 cheese slices in each packet.
There are 12 burgers in each box.

Rita buys exactly the same number of cheese slices and burgers.

i)
How many packets of cheese slices and how many boxes of burgers does she buy?

[3]

Rita wants to put one cheese slice and one burger into each bread roll.
She wants to use all the cheese slices and all the burgers.

ii)
How many bread rolls does Rita need?
[1]

Did this page help you?

3
Sme Calculator
3 marks

Matt and Dan cycle around a cycle track.

  Each lap Matt cycles takes him 50 seconds.
  Each lap Dan cycles takes him 80 seconds.

  Dan and Matt start cycling at the same time at the start line.

  Work out how many laps they will each have cycled when they are next at the start line together.

Did this page help you?

4a
Sme Calculator
3 marks

Express 180 as a product of its prime factors.

4b
Sme Calculator
2 marks

Martin thinks of two numbers.

He says,

"The Highest Common Factor (HCF) of my two numbers is 6
The Lowest Common Multiple (LCM) of my two numbers is a multiple of 15"

Write down two possible numbers that Martin is thinking of.

Did this page help you?

5
Sme Calculator
2 marks

Find the highest common factor (HCF) of 72 and 90.

Did this page help you?

6
Sme Calculator
2 marks

c equals 2 to the power of 10 cross times 3 cross times 5 to the power of 6

Work out 18 c.

Give your answer as a product of prime factors in index form.

Did this page help you?

7
Sme Calculator
2 marks

Work out the highest common factor (HCF) of 75 and 105.

Did this page help you?

8
Sme Calculator
2 marks

Work out the lowest common multiple (LCM) of 120 and 144.

Did this page help you?

9a
Sme Calculator
2 marks

Written as the product of its prime factors

672 space equals space 2 to the power of 5 space end exponent cross times space 3 space cross times space 7

Write 252 as the product of its prime factors.

9b
Sme Calculator
1 mark

Work out the value of the highest common factor of 672 and 252.

Did this page help you?

10
Sme Calculator
4 marks

At a railway station, trains are either eastbound or westbound.
An eastbound train leaves the station every 25 minutes.
A westbound train leaves the station every 45 minutes.

An eastbound train and a westbound train both leave the station at 8am.

When is the next time that two trains leave the station together?

Did this page help you?

11a
Sme Calculator
4 marks

A bus timetable shows the following information.

  • A bus following route T leaves for the train station every 20 minutes.
  • A bus following route A leaves for the airport every 18 minutes.
  • A bus following route T and a bus following route A both leave at 8.37 am.

When is the next time one of each bus is timetabled to leave at the same time?

11b
Sme Calculator
1 mark

Write down one assumption that was necessary to solve this problem.

Did this page help you?

12a
Sme Calculator
5 marks
i)
Write 120 as a product of its prime factors.
[3]
ii)
The lowest common multiple (LCM) of x and 120 is 360.
Find the smallest possible value of x.
[2]
12b
Sme Calculator
2 marks

Two numbers, A and B, are written as a product of prime factors.

      A space equals space 2 to the power of 4 space cross times 3 squared space cross times space 7 squared      B space equals space 2 cubed space cross times space 3 space cross times space 5 cross times space 7

Find the highest common factor (HCF) of A and B.

Did this page help you?

13
Sme Calculator
2 marks

Find the lowest common multiple (LCM) of 180 and 504.

Did this page help you?

14a
Sme Calculator
3 marks

N space equals space 480 space cross times space 10 to the power of 9

Write N as a product of powers of its prime factors.
Show your working clearly.

14b
Sme Calculator
1 mark

Find the largest factor of N that is an odd number.

Did this page help you?

15a
Sme Calculator
2 marks

A equals space 3 squared space cross times space 5 to the power of 4 space cross times space 7 space space space space space space space space space space space space space space space space space space space space space B space equals space 3 to the power of 4 space cross times space 5 cubed space cross times space 7 space cross times space 11

Find the highest common factor (HCF) of space A space and B.

15b
Sme Calculator
2 marks

Find the lowest common multiple (LCM) of A and B.

Did this page help you?

16
Sme Calculator
2 marks

A space equals space 3 to the power of 5 cross times space 5 space cross times space 7 to the power of 3 space end exponent
B space equals space 2 cubed cross times space 3 space cross times space 7 to the power of 4

i)
Find the Highest Common Factor (HCF) of A and B.

ii)
Find the Lowest Common Multiple (LCM) of space A spaceand B.

Did this page help you?

17
Sme Calculator
2 marks

Work out the lowest common multiple (LCM) of 36 and 120.

Did this page help you?

18
Sme Calculator
2 marks

table row blank blank cell A space equals space 2 cubed cross times 3 squared cross times 5 squared cross times 11
B space equals space 2 to the power of 4 cross times 3 cross times 5 to the power of 4 cross times 13 end cell end table

Find the lowest common multiple (LCM) of space A spaceand B.
Give your answer as a product of powers of prime numbers.

Did this page help you?

19
Sme Calculator
3 marks

A machine has a buzzer that sounds every 50 minutes.
The machine also has a bell that sounds every 80 minutes.

The buzzer and the bell sound together at 10 am.

Find the time at which they next sound together.

Did this page help you?

1a
Sme Calculator
2 marks

Find the lowest common multiple (LCM) of 40 and 56.

1b
Sme Calculator
1 mark

A equals 2 cubed cross times 3 cross times 5         B equals 2 squared cross times 3 cross times 5 squared

Write down the highest common factor (HCF) of A and B.

Did this page help you?

2
Sme Calculator
3 marks

Here are three lamps.

image-15

Lamp A flashes every 20 seconds.
Lamp B flashes every 45 seconds.
Lamp C flashes every 120 seconds.

The three lamps start flashing at the same time.

How many times in one hour will the three lamps flash at the same time?

Did this page help you?

3
Sme Calculator
5 marks

Ali is planning a party.

He wants to buy some cakes and some sausage rolls.

The cakes are sold in boxes.
There are 12 cakes in each box.
Each box of cakes costs £2.50

The sausage rolls are sold in packs.
There are 8 sausage rolls in each pack.
Each pack of sausage rolls costs £1.20

Ali wants to buy more than 60 cakes and more than 60 sausage rolls.
He wants to buy exactly the same number of cakes as sausage rolls.

What is the least amount of money Ali will have to pay?

Did this page help you?

4
Sme Calculator
3 marks

John buys some boxes of pencils and some packets of pens for people to use at a conference.

There are 40 pencils in a box.
There are 15 pens in a packet.

John gives one pencil and one pen to each person at the conference.
He has no pencils left.
He has no pens left.

How many boxes of pencils and how many packets of pens did John buy?

Did this page help you?

5
Sme Calculator
3 marks

Liz buys packets of coloured buttons.

There are 8 red buttons in each packet of red buttons.
There are 6 silver buttons in each packet of silver buttons.
There are 5 gold buttons in each packet of gold buttons.

Liz buys equal numbers of red buttons, silver buttons and gold buttons.

How many packets of each colour of buttons did Liz buy?

................................. packets of red buttons

  ............................ packets of silver buttons

............................... packets of gold buttons

Did this page help you?

6
Sme Calculator
4 marks

a is a common factor of 72 and 120.

b is a common multiple of 6 and 9.

Work out the highest possible value of  a over b.

Did this page help you?

7
Sme Calculator
3 marks

N is a number.

As a product of prime factors in index form    N space equals space 2 space cross times space 3 to the power of 4 space cross times space y cubed

Work out 3 N squared as a product of prime factors in index form.

Give your answer in terms of y.

Did this page help you?

8
Sme Calculator
5 marks

A clock chimes every 20 minutes.
A light flashes every 8 minutes.
The clock chimes and the light flashes together at 08:00.

How many times between 08:01 and 12:30 will the clock chime and the light flash together?
Show your working.

Did this page help you?

9
Sme Calculator
3 marks

Given that 168 equals 2 cubed cross times 3 cross times 7, find the lowest common multiple (LCM) of 168 and 30.

Did this page help you?

10
Sme Calculator
2 marks

You are given that

begin mathsize 16px style 90 equals 3 squared cross times 2 cross times 5 end style and 177147 equals 3 to the power of 11

Find the lowest common multiple (LCM) of 270 and 177147.
Give your answer using power notation and as an ordinary number.

using power notation .............................................................
as an ordinary number ...................................................

Did this page help you?

11a
Sme Calculator
4 marks

Two numbers, P and Q, are written as products of their prime factors

         P space equals space 2 to the power of 5 space cross times space 3 squared space cross times 5 cubed space cross times 11         Q space equals space 2 to the power of 4 space cross times 3 space cross times 5 to the power of 4 space cross times 7

i)
Find the lowest common multiple (LCM) of P and Q.
[2]
ii)
The number C is written as the product of its prime factors.

   
C equals space 2 cubed cross times 3 cross times 5 squared

Work out P space divided by space C , leaving your answer as a product of powers of prime numbers.

[2]

11b
Sme Calculator
6 marks
i)
Write 450 as a product of its prime factors.
[3]

ii)
Find the highest common factor (HCF) of 270 and 450.
[3]

Did this page help you?

12
Sme Calculator
4 marks

Here are some properties of a number.

  • It is a common factor of 288 and 360.
  • It is a common multiple of 4 and 6.
  • It is larger than 25.

Find the two possible numbers with these properties.

Did this page help you?

13
Sme Calculator
2 marks

A space equals space 5 squared space cross times space 7 to the power of 4 space cross times space 11 to the power of p
B space equals space 5 to the power of m space cross times space 7 to the power of n – 5 end exponent space cross times space 11

m comma space n spaceand p are integers such that
m space greater than space 2
n space greater than space 10
p space greater than space 1

Find the highest common factor (HCF) of A and B
Give your answer as a product of powers of its prime factors.

Did this page help you?

14a
Sme Calculator
2 marks

Find the highest common factor left parenthesis HCF right parenthesis of 96 and 120.

14b
Sme Calculator
2 marks

table row cell A space end cell equals cell space 2 cubed space cross times space 5 space cross times space 7 squared space cross times space 11 space end cell row cell B space end cell equals cell space 2 to the power of 4 space cross times space 7 space cross times space 11 space end cell row cell C space end cell equals cell space 3 space cross times space 5 squared end cell end table

Find the lowest common multiple left parenthesis LCM right parenthesis of A comma space B and C.

Did this page help you?

15
Sme Calculator
2 marks

table row cell A space end cell equals cell space 3 to the power of 5 cross times space 5 space cross times space 7 cubed space end cell row cell B space end cell equals cell space 2 cubed cross times space 3 space cross times space 7 to the power of 4 space end cell row cell C space end cell equals cell space 2 to the power of p cross times space 5 to the power of q cross times space 7 to the power of r end cell end table

Given that

the HCF of B and C is 23× 7
the LCM of A and C is 24× 35× 52× 73

Find the value of p comma the value of q and the value of r.

p space equals .......................................................
q space equals .......................................................
r space equals .......................................................

Did this page help you?

16
Sme Calculator
1 mark

Here is a list of five numbers.
 

98 to the power of 53 space space space space space space space space 98 to the power of 64 space space space space space space space space 98 to the power of 73 space space space space space space space space 98 to the power of 88 space space space space space space space space 98 to the power of 91
 

Find the lowest common multiple of these five numbers.

Did this page help you?