Question

How do you write 98 as a product of prime factors?

Answer 1

`98 = 2*7*7`

Explanation:

Since `98` ends with an even digit, we can tell that it is divisible by `2`:

`98/2 = 49`

Try each possible prime factor in turn:

• `49` ends in an odd digit, so is not divisible by `2`.

• The sum of its digits is `4+9 = 13`, which is not divisible by `3`, so `49` is not divisible by `3` either.

• `49` does not ends with `5` or `0`, so is not divisible by `5`.

• `49` is divisible by `7`. We find:

  `49/7 = 7`

So:

`98 = 2*7*7`

We can also draw this as a factor tree:

`color(white)(00000)98`
`color(white)(0000)"/"color(white)(00)"\"`
`color(white)(000)2color(white)(000)49`
`color(white)(000000)"/"color(white)(00)"\"`
`color(white)(00000)7color(white)(0000)7`