Q: What are the factors or divisors of the number 456?

 A: 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456

How do I find the factors or divisors of the number 456?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the factors of larger numbers. To find the factors of the number 456, it is easiest to start from the outside in. Here's what we mean:

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table.

1 456

Next, we take the number 456 and divide it by 2.

In this case, 2 ÷ 456 = 228

If the quotient is a whole number, then 2 and 228 are factors. Write them in the table below. If the quotient is not a whole number, skip to the next test.

1 2 228 456

Now, we try dividing 456 by 3.

456 ÷ 3 = 152

If the quotient is a whole number, then 3 and 152 are factors. Write them in the table below. If the quotient is not a whole number, skip to the next test.

Here is what our table should look like at this step:

1 2 3 152 228 456

Let's try dividing by 4.

456 ÷ 4 = 114

If the quotient is a whole number, then 4 and 114 are factors. Write them in the table below. If the quotient is not a whole number, skip to the next test.

Here is what our table should look like at this step:

1 2 3 4 114 152 228 456

We keep dividing by the next largest number, in this case the number 5. If the quotient of 5 ÷ 456 is a whole number, then 5 and your quotient are factors of the number.


Keep dividing by the next highest number until you cannot divide anymore.


What you will end up with is this table:

123468121924385776114152228456

All of the numbers in the table above can be evenly divided into the number 456.

Finally, for your reference, here are all of the divisor combinations of the number 456:

1 x 4562 x 2283 x 1524 x 1146 x 768 x 5712 x 3819 x 24

More Examples

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