Question

How do you write 78 as a product of prime factors?

Answer 1

`78 = 2 * 3 * 13`

Explanation:

Given `78` to factorise

• `78` ends with an even digit, so is divisible by `2` and we find:
  `78 = 2 * 39color(white)(0/0)`

• `39` ends with an odd digit, so is not divisible by `2`.

• The digits of `39` add up to a multiple of `3`, namely `3+9 = 12`. So we can tell that `39` is divisible by `3`:
  `39 = 3 * 13color(white)(0/0)`

• `13` is a prime number, not divisible by any number greater than `1` or less than `13`.

So the prime factorisation of `78` is:

`78 = 2 * 3 * 13`

This can also be represented by a factor tree:

`color(white)(0000)78`
`color(white)(000)"/"color(white)(00)"\"`
`color(white)(00)2color(white)(000)39`
`color(white)(00000)"/"color(white)(00)"\"`
`color(white)(0000)3color(white)(000)13`