Q: What are the factor combinations of the number 100,012,297?

 A:
Positive:   1 x 1000122977 x 1428747111 x 909202777 x 1298861157 x 6370211099 x 910031727 x 579118273 x 12089
Negative: -1 x -100012297-7 x -14287471-11 x -9092027-77 x -1298861-157 x -637021-1099 x -91003-1727 x -57911-8273 x -12089


How do I find the factor combinations of the number 100,012,297?

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 100,012,297, 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.

1 100,012,297
-1 -100,012,297

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 100,012,297.

Example:
1 x 100,012,297 = 100,012,297
and
-1 x -100,012,297 = 100,012,297
Notice both answers equal 100,012,297

With that explanation out of the way, let's continue. Next, we take the number 100,012,297 and divide it by 2:

100,012,297 ÷ 2 = 50,006,148.5

If the quotient is a whole number, then 2 and 50,006,148.5 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:

1 100,012,297
-1 -100,012,297

Now, we try dividing 100,012,297 by 3:

100,012,297 ÷ 3 = 33,337,432.3333

If the quotient is a whole number, then 3 and 33,337,432.3333 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:

1 100,012,297
-1 -100,012,297

Let's try dividing by 4:

100,012,297 ÷ 4 = 25,003,074.25

If the quotient is a whole number, then 4 and 25,003,074.25 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:

1 100,012,297
-1 100,012,297
Keep dividing by the next highest number until you cannot divide anymore.

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

1711771571,0991,7278,27312,08957,91191,003637,0211,298,8619,092,02714,287,471100,012,297
-1-7-11-77-157-1,099-1,727-8,273-12,089-57,911-91,003-637,021-1,298,861-9,092,027-14,287,471-100,012,297

More Examples

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