Q: What are the factor combinations of the number 109,465,315?

 A:
Positive:   1 x 1094653155 x 2189306343 x 254570571 x 1541765101 x 1083815215 x 509141355 x 308353505 x 2167633053 x 358554343 x 252055041 x 217157171 x 15265
Negative: -1 x -109465315-5 x -21893063-43 x -2545705-71 x -1541765-101 x -1083815-215 x -509141-355 x -308353-505 x -216763-3053 x -35855-4343 x -25205-5041 x -21715-7171 x -15265


How do I find the factor combinations of the number 109,465,315?

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 109,465,315, 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.

1 109,465,315
-1 -109,465,315

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 109,465,315.

Example:
1 x 109,465,315 = 109,465,315
and
-1 x -109,465,315 = 109,465,315
Notice both answers equal 109,465,315

With that explanation out of the way, let's continue. Next, we take the number 109,465,315 and divide it by 2:

109,465,315 ÷ 2 = 54,732,657.5

If the quotient is a whole number, then 2 and 54,732,657.5 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:

1 109,465,315
-1 -109,465,315

Now, we try dividing 109,465,315 by 3:

109,465,315 ÷ 3 = 36,488,438.3333

If the quotient is a whole number, then 3 and 36,488,438.3333 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:

1 109,465,315
-1 -109,465,315

Let's try dividing by 4:

109,465,315 ÷ 4 = 27,366,328.75

If the quotient is a whole number, then 4 and 27,366,328.75 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:

1 109,465,315
-1 109,465,315
Keep dividing by the next highest number until you cannot divide anymore.

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

1543711012153555053,0534,3435,0417,17115,26521,71525,20535,855216,763308,353509,1411,083,8151,541,7652,545,70521,893,063109,465,315
-1-5-43-71-101-215-355-505-3,053-4,343-5,041-7,171-15,265-21,715-25,205-35,855-216,763-308,353-509,141-1,083,815-1,541,765-2,545,705-21,893,063-109,465,315

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