Q: What are the factor combinations of the number 21,736,435?

 A:
Positive:   1 x 217364355 x 43472877 x 310520535 x 62104161 x 356335305 x 71267427 x 509052135 x 10181
Negative: -1 x -21736435-5 x -4347287-7 x -3105205-35 x -621041-61 x -356335-305 x -71267-427 x -50905-2135 x -10181


How do I find the factor combinations of the number 21,736,435?

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 21,736,435, 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 21,736,435
-1 -21,736,435

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 21,736,435.

Example:
1 x 21,736,435 = 21,736,435
and
-1 x -21,736,435 = 21,736,435
Notice both answers equal 21,736,435

With that explanation out of the way, let's continue. Next, we take the number 21,736,435 and divide it by 2:

21,736,435 ÷ 2 = 10,868,217.5

If the quotient is a whole number, then 2 and 10,868,217.5 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 21,736,435
-1 -21,736,435

Now, we try dividing 21,736,435 by 3:

21,736,435 ÷ 3 = 7,245,478.3333

If the quotient is a whole number, then 3 and 7,245,478.3333 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 21,736,435
-1 -21,736,435

Let's try dividing by 4:

21,736,435 ÷ 4 = 5,434,108.75

If the quotient is a whole number, then 4 and 5,434,108.75 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 21,736,435
-1 21,736,435
Keep dividing by the next highest number until you cannot divide anymore.

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

15735613054272,13510,18150,90571,267356,335621,0413,105,2054,347,28721,736,435
-1-5-7-35-61-305-427-2,135-10,181-50,905-71,267-356,335-621,041-3,105,205-4,347,287-21,736,435

More Examples

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