Q: What are the factors or divisors of the number 30,972?

How do I find the factors or divisors of the number 30,972?

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 30,972, 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

30,972

Next, we take the number 30,972 and divide it by 2.

In this case, 30,972 ÷ 2 = 15,486

If the quotient is a whole number, then 2 and 15,486 are factors. Write them in the table below. If the quotient is not a whole number, skip to the next test.

Now, we try dividing 30,972 by 3.

30,972 ÷ 3 = 10,324

If the quotient is a whole number, then 3 and 10,324 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:

Let's try dividing by 4.

30,972 ÷ 4 = 7,743

If the quotient is a whole number, then 4 and 7,743 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:

We keep dividing by the next largest number, in this case the number 5. If the quotient of 30,972 ÷ 5 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:

All of the numbers in the table above can be evenly divided into the number 30,972.

Finally, for your reference, here are all of the divisor combinations of the number 30,972:

1 x 309722 x 154863 x 103244 x 77436 x 516212 x 258129 x 106858 x 53487 x 35689 x 348116 x 267174 x 178

More Examples

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