Syllabus Edition

First teaching 2021

Last exams 2024

|

Prime Factors, HCF & LCM (CIE IGCSE Maths: Extended)

Exam Questions

2 hours41 questions
1
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2 marks

Write 84 as a product of its prime factors.

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2
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3 marks

Write 525 as a product of its prime factors.

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3
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2 marks

Express 56 as the product of its prime factors.

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4
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2 marks

Write 36 as a product of its prime factors.

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5
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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?

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6
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3 marks

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

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7
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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.

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8a
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3 marks

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

8b
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1 mark

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

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9
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3 marks

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

Show your working clearly.

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10
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2 marks

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

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11
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3 marks

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

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12
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3 marks

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

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13
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3 marks

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

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1
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2 marks

Find the highest common factor (HCF) of 84 and 105.

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2
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2 marks

Find the highest common factor (HCF) of 90 and 48.

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3a
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2 marks

Write 56 as a product of its prime factors.

3b
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2 marks

Find the lowest common multiple (LCM) of 56 and 42.

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4
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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?

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5
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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?

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?

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6
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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.

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7a
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3 marks

Express 180 as a product of its prime factors.

7b
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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.

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8
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2 marks

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

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9a
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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.

9b
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2 marks

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

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10
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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.

[1]

ii)
Find the Lowest Common Multiple (LCM) of space A spaceand B.
[1]

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11
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2 marks

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

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12
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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.

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13
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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.

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14
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2 marks

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

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15
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2 marks

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

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16a
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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.

16b
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1 mark

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

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1
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1 mark

Find the highest odd number that is a factor of 60 and a factor of 90.

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2
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1 mark

234 equals 2 cross times 3 squared cross times 13 space space space space space space space space space space space space space 1872 equals 2 to the power of 4 cross times 3 squared cross times 13 space space space space space space space space space space space space space 234 cross times 1872 equals 438 space 048


Use this information to write 438 048 as a product of its prime factors.

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3
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2 marks

N equals 2 to the power of 4 cross times 3 cross times 7 to the power of 5

P N equals K, where P is an integer and K is a square number.
 
Find the smallest value of P.
 

P equals ................................................ 

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4
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3 marks

Here are three lamps.

q4-1-3-hard-ocr-gcse-maths-extended

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?

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5
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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

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6
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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?

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7
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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?

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8a
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2 marks

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

8b
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1 mark

A space equals space 2 cubed space cross times space 3 space cross times space 5 space 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 2 to the power of 2 space end exponent cross times space 3 space cross times space 5 squared

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

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9
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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.

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10a
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2 marks

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

10b
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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.

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11
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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 ....................................................... 

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12
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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.

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