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## Finding All Factors Of A Number

In order to find the factors of a number simply used one of the divisibility or multiplication methods explained below.

### How to Factor A Number With Divisibility?

We want to find all of the whole numbers that your number is divisible by. Start dividing your number one after another with all numbers that are smaller than itself(Example: for 45 you would have to make half(23) the number of divisions). All numbers that leave no remainder after division are factors of the number!

This is a simple yet also a very time consuming method. Not practical to use when dealing with large numbers.

### How To Factor A Number With Multiplication?

To find all the factors of a given number you start by multiplying with 1* (Example 1*22=22) then with 2*x, 3*x, 4*x and so on. A pair of numbers that when multiplied together equals 22 can be called factors of 22(a factor pair of this integer).

This is also called the rainbow method, because you can write the smaller factors on the left and the bigger factors on the right side.

Gradually these factors will start to close in on each other. Once the gap between big and small factors is closed and they start to meet you know that all factors are found.

## Tips For Finding Factors Easily

Simplify math by using these six tips for finding factors the easy way.

Tip 1: If the last digit of a bigger number is 0, 2, 4, 6 or 8 then this means that the whole number is an even number. If it is an even number it is divisible by 2(making 2 a factor).

Tip 2: By multiplying the prime factors of a given number, we can find new factors.

Tip 3: If the sum of digits of a number is divisible by 3 then the number is also divisible by 3(making 3 a factor). Example: the digits of 24 are 2 and 4 so 2+4=6 and 6 is divisible by 3, meaning that 12 is divisible by 3). Same logic works also for number 9.

Tip 4: If the last two digits of a number are 00 then this number is divisible by 4(knowing multiples of 4 comes in handy when using this). Making 4 a factor.

Tip 5: If the last digit of a number is 0 or 5 then 5 is a factor of this number, because it is divisible.

Tip 6: All numbers that are divisible by both 2 and 3 are also divisible by 6. By using our third and sixth tip together you can now easily check if 6 is a factor in a big number.

## What Are Factors Of A Number?

Whole numbers that are divisible without leaving any fractional part or remainder are called factors of a number. A factor of a number is also called it's divisor.