Q: What are the factor combinations of the number 17,671,225?

 A:
Positive:   1 x 176712255 x 353424511 x 160647513 x 135932525 x 70684955 x 32129565 x 271865143 x 123575275 x 64259325 x 54373715 x 247153575 x 4943
Negative: -1 x -17671225-5 x -3534245-11 x -1606475-13 x -1359325-25 x -706849-55 x -321295-65 x -271865-143 x -123575-275 x -64259-325 x -54373-715 x -24715-3575 x -4943


How do I find the factor combinations of the number 17,671,225?

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 17,671,225, 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 17,671,225
-1 -17,671,225

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 17,671,225.

Example:
1 x 17,671,225 = 17,671,225
and
-1 x -17,671,225 = 17,671,225
Notice both answers equal 17,671,225

With that explanation out of the way, let's continue. Next, we take the number 17,671,225 and divide it by 2:

17,671,225 ÷ 2 = 8,835,612.5

If the quotient is a whole number, then 2 and 8,835,612.5 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 17,671,225
-1 -17,671,225

Now, we try dividing 17,671,225 by 3:

17,671,225 ÷ 3 = 5,890,408.3333

If the quotient is a whole number, then 3 and 5,890,408.3333 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 17,671,225
-1 -17,671,225

Let's try dividing by 4:

17,671,225 ÷ 4 = 4,417,806.25

If the quotient is a whole number, then 4 and 4,417,806.25 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 17,671,225
-1 17,671,225
Keep dividing by the next highest number until you cannot divide anymore.

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

1511132555651432753257153,5754,94324,71554,37364,259123,575271,865321,295706,8491,359,3251,606,4753,534,24517,671,225
-1-5-11-13-25-55-65-143-275-325-715-3,575-4,943-24,715-54,373-64,259-123,575-271,865-321,295-706,849-1,359,325-1,606,475-3,534,245-17,671,225

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