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1.1 Factors, multiples and primes

1.1 Factors, multiples and primes

In this section you will … Key words

• write a positive integer as a product of prime factors factor tree
• use prime factors to find a highest common factor highest common
(HCF) and a lowest common multiple (LCM). factor (HCF)

index
Any integer bigger than 1:
• is a prime number, or integer
• can be written as a product of prime numbers. lowest common
Example: multiple (LCM)

46 = 2 × 23 47 is prime 48 = 2 × 2 × 2 × 2 × 3 prime factor
49 = 7 × 7 50 = 2 × 5 × 5
You can use a factor tree to write an integer as a product of its 120

prime factors.
This is how to draw a factor tree for 120. 12 10
1 Write 120.
2 Draw branches to two numbers that have a product of 120. Do 3 4 2 5
not use 1 as one of the numbers. Here we have chosen 12 and 10. 2 2

×
=
120 12 10
3 Do the same with 12 and 10. Here 12 = 3 × 4 and 10 = 2 × 5
4 3, 2 and 5 are prime numbers, so circle them.
5 Draw two more branches from 4. 4 = 2 × 2. Circle the 2s.

6 Now all the end numbers are prime, so stop.
7 120 is the product of all the end numbers: 120 = ××× ×
2 35
2
2
8 You can check that this is correct using a calculator.
×
You can also write the result like this: 120 = 2 × 3 5
3
2 means 2 × 2 × 2 and the small 3 is an index.
3
=×
Now check that 753 5 2
You can use products of prime factors to find the HCF and LCM of two
numbers.

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