### 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.