# Video: Pack 2 • Paper 1 • Question 1

Pack 2 • Paper 1 • Question 1

02:14

### Video Transcript

Write 48 as a product of prime factors.

A prime number has only two factors: itself and one. The first five prime numbers are two, three, five, seven, and 11. Two is a prime number as it is only divisible by one and two. Likewise, three is a prime number as it is only divisible by one and three. The same is true for five, seven, and 11. They are only divisible by one and themselves.

In our example, we’re asked to write 48 as a product of prime factors. Which of the prime factors divides exactly into 48? Well, the most obvious answer is two as 48 is even. Two multiplied by 24 is equal to 48. As two is prime, we will circle it. We now need to split 24. Which of the prime numbers divides into 24? As 24 is also even, two must divide into 24. Two multiplied by 12 is equal to 24. We can then repeat this step by dividing 12 by two. Two multiplied by six is equal to 12. Six has factors two and three. Two multiplied by three is equal to six. As three is also a prime number, we need to circle this as the only factors of three are one and three.

48 can therefore be written as two multiplied by two multiplied by two multiplied by two multiplied by three. This can be simplified to two to the power of four multiplied by three. 48 written as a product of prime factors in index form is two to the power of four multiplied by three.

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