Q: What are the factor combinations of the number 21,537,635?

 A:
Positive:   1 x 215376355 x 43075277 x 307680535 x 615361173 x 124495865 x 248991211 x 177853557 x 6055
Negative: -1 x -21537635-5 x -4307527-7 x -3076805-35 x -615361-173 x -124495-865 x -24899-1211 x -17785-3557 x -6055


How do I find the factor combinations of the number 21,537,635?

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 divisors of larger numbers. To find the factor combinations of the number 21,537,635, it is easier to work with a table - it's called factoring from the outside in.

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. Then, below that, write the numbers as a negative as well.

1 21,537,635
-1 -21,537,635

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 21,537,635.

Example:
1 x 21,537,635 = 21,537,635
and
-1 x -21,537,635 = 21,537,635
Notice both answers equal 21,537,635

With that explanation out of the way, let's continue. Next, we take the number 21,537,635 and divide it by 2:

21,537,635 ÷ 2 = 10,768,817.5

If the quotient is a whole number, then 2 and 10,768,817.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 21,537,635
-1 -21,537,635

Now, we try dividing 21,537,635 by 3:

21,537,635 ÷ 3 = 7,179,211.6667

If the quotient is a whole number, then 3 and 7,179,211.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 21,537,635
-1 -21,537,635

Let's try dividing by 4:

21,537,635 ÷ 4 = 5,384,408.75

If the quotient is a whole number, then 4 and 5,384,408.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 21,537,635
-1 21,537,635
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

157351738651,2113,5576,05517,78524,899124,495615,3613,076,8054,307,52721,537,635
-1-5-7-35-173-865-1,211-3,557-6,055-17,785-24,899-124,495-615,361-3,076,805-4,307,527-21,537,635

More Examples

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