HCFs, LCMs and Prime Factors
1.	(a)	Write 28 as the product of its prime factors.
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(2)
 (b)	Find the least common multiple (LCM) of 28 and 42.
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Answer...............................................................................
(2)
(Total 4 marks)
2.	(a)	Write 18 as the product of its prime factors.
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Answer ………………………………
(2)
(b)	What is the least common multiple (LCM) of 12 and 18?
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Answer ……………………………….
(1)
(Total 3 marks)
3.	(a)	Express 36 as a product of its prime factors.
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Answer ................................................
(3)
 (b)	Find the Highest Common Factor (HCF) of 36 and 60.
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(2)
(Total 5 marks)
4.	(a)	Express 144 as the product of its prime factors.
Write your answer in index form.
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Answer ..................................................................
(3)
(b)	Find the Highest Common Factor (HCF) of 60 and 144.
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Answer ..................................................................
(2)
(Total 5 marks)
5.	Express 120 as the product of its prime factors. 
Give your answer in index form.

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Answer ............................................................
(Total 3 marks)
6.	When written as the product of prime factors	
(a)	Write 150 as the product of prime factors.
Give your answer in index form.
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Answer ……………………………………………………
(3)
 (b)	Work out the highest common factor (HCF) of 225 and 150.
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Answer ……………………………………………………
(2)
(Total 5 marks)
7.	Express 360 as a product of its prime factors.
Give your answer in index form.
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Answer .....................................................
(Total 3 marks)
8.	Jenny is organising a barbecue.
There are 30 bread rolls in a pack.
There are 16 sausages in a pack.
She needs exactly the same number of bread rolls as sausages.
What is the smallest number of each pack she must buy?
You must show all your working.
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Answer ........................ packs of rolls
and ....................... packs of sausages
(Total 3 marks)
9.	Tom, Sam and Matt are counting drum beats.
	Tom hits a snare drum every 2 beats.
Sam hits a kettle drum every 5 beats.
Matt hits a bass drum every 8 beats.
	Tom, Sam and Matt start by hitting their drums at the same time.
How many beats is it before Tom, Sam and Matt next hit their drums at the same time?
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Answer .............................................................. beats
(Total 2 marks)
10.	Polly Parrot squawks every 12 seconds.
Mr Toad croaks every 21 seconds.
They both make a noise at the same time.
After how many seconds will they next make a noise at the same time?
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Answer …………………………………………… seconds
(Total 2 marks)
 
11.	(a)	24 can be written as 24 = 2a × 3
	What is the value of a?
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Answer a = .................................................................................................................
(1)
(b)	A box measures 24 cm by 18 cm by 15 cm.
The box is to be filled with cubes of equal size.
	What is the length of the side of the largest cube that could be used to fill the box?
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Answer .................................................... cm
(2)
(Total 3 marks)