# Video: Pack 1 • Paper 1 • Question 2

Pack 1 • Paper 1 • Question 2

01:25

### Video Transcript

Write 56 as a product of prime factors.

To answer this question, we need to draw a factor tree. We’ll start by thinking of any pair of factors of 56. 56 is equal to two multiplied by 28. You could use any other pair of factors of 56 at this point, for example, four and 14. Two is a prime number. So we’ll circle it and this branch of the factor tree stops here.

28 isn’t a prime number. So we need to continue this branch of the factor tree. We think of a pair of factors of 28. 28 is equal to four multiplied by seven. And as seven is a prime number, we circle it and this branch of the factor tree stops here.

Four, however, isn’t a prime number. So we need to continue this branch of the factor tree and break it down into the product of two and two, which are prime numbers. We’ve now found all of the prime factors of 56. So we can write 56 as a product: two multiplied by two multiplied by two multiplied by seven. We can express this product in index form as two multiplied by two multiplied by two can be written as two cubed.

As a product of prime factors, 56 is equal to two cubed multiplied by seven.