# Factors of 17: Factor Pairs, Factor Tree

The Factors are divisors through which you can divide a particular number after which there are no remainders. 17 is a Prime Number and in this blog, we shall learn about the Factors of 17, and whether 17 has any factors other than 1 and itself! Furthermore, the Factors of Negative 17, Factor Pairs, Factor tree and finding the Factors of 17 via the Division Method.

## What are the Factors of 17?

Factors of a number are integers that divide evenly into that number, hence leaving no remainder. In the case of 17, there are only two factors which are 1 and 17 itself.

Why are there only two? Because 17 is a Prime number. Additionally, Prime numbers have exactly two factors which are 1 and the number itself. Moreover, they cannot be broken down further into smaller whole numbers without leaving a remainder.

## What are the Factors of -17?

The factors of Negative -17 are the same as the Factors of 17. Hence, they are 1 and -17.

Here is the reasoning:

• 1 x -17 = -17 (positive times negative equals negative)
• -17 x 1 = -17 (negative times positive equals negative)

Therefore, both 1 and -17 divide into -17 with no remainder.

## Factors of 17 in Pairs

When considering Factors, you can also think about them in pairs. Any two numbers that multiply to give 17 are considered factor pairs.

In this case, the only Factor pair for 17 is (1, 17).

Moreover, you can include Negative factors as well, thus resulting in another pair which is (-1, -17).

## What is the Factor Tree of 17?

A Factor tree is a visual representation of a particular number’s factors. As 17 is a Prime number, it cannot be broken down further. Therefore, its Factor tree would simply consist of 17 at the top, with no branches below it.

## Factors of 17 by Division Method

The Division method is a way to find a particular number’s factors.

• You simply try dividing the number by consecutive positive integers until you either reach the number itself or encounter a remainder.
• In the case of 17, you will only find two divisions that result in no remainder:

17 ÷ 1 = 17 (no remainder)

17 ÷ 17 = 1 (no remainder)

Moreover, any other division attempt will leave a remainder, signifying that the number is not a factor of 17.