Q: What are the factor combinations of the number 35,646,415?

 A:
Positive:   1 x 356464155 x 71292837 x 509234535 x 1018469113 x 315455565 x 63091791 x 450653955 x 9013
Negative: -1 x -35646415-5 x -7129283-7 x -5092345-35 x -1018469-113 x -315455-565 x -63091-791 x -45065-3955 x -9013


How do I find the factor combinations of the number 35,646,415?

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 35,646,415, 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 35,646,415
-1 -35,646,415

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 35,646,415.

Example:
1 x 35,646,415 = 35,646,415
and
-1 x -35,646,415 = 35,646,415
Notice both answers equal 35,646,415

With that explanation out of the way, let's continue. Next, we take the number 35,646,415 and divide it by 2:

35,646,415 ÷ 2 = 17,823,207.5

If the quotient is a whole number, then 2 and 17,823,207.5 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 35,646,415
-1 -35,646,415

Now, we try dividing 35,646,415 by 3:

35,646,415 ÷ 3 = 11,882,138.3333

If the quotient is a whole number, then 3 and 11,882,138.3333 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 35,646,415
-1 -35,646,415

Let's try dividing by 4:

35,646,415 ÷ 4 = 8,911,603.75

If the quotient is a whole number, then 4 and 8,911,603.75 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 35,646,415
-1 35,646,415
Keep dividing by the next highest number until you cannot divide anymore.

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

157351135657913,9559,01345,06563,091315,4551,018,4695,092,3457,129,28335,646,415
-1-5-7-35-113-565-791-3,955-9,013-45,065-63,091-315,455-1,018,469-5,092,345-7,129,283-35,646,415

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