Q: What are the factor combinations of the number 101,132,015?

 A:
Positive:   1 x 1011320155 x 2022640347 x 2151745235 x 430349337 x 3000951277 x 791951685 x 600196385 x 15839
Negative: -1 x -101132015-5 x -20226403-47 x -2151745-235 x -430349-337 x -300095-1277 x -79195-1685 x -60019-6385 x -15839


How do I find the factor combinations of the number 101,132,015?

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 101,132,015, 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.

1 101,132,015
-1 -101,132,015

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 101,132,015.

Example:
1 x 101,132,015 = 101,132,015
and
-1 x -101,132,015 = 101,132,015
Notice both answers equal 101,132,015

With that explanation out of the way, let's continue. Next, we take the number 101,132,015 and divide it by 2:

101,132,015 ÷ 2 = 50,566,007.5

If the quotient is a whole number, then 2 and 50,566,007.5 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:

1 101,132,015
-1 -101,132,015

Now, we try dividing 101,132,015 by 3:

101,132,015 ÷ 3 = 33,710,671.6667

If the quotient is a whole number, then 3 and 33,710,671.6667 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:

1 101,132,015
-1 -101,132,015

Let's try dividing by 4:

101,132,015 ÷ 4 = 25,283,003.75

If the quotient is a whole number, then 4 and 25,283,003.75 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:

1 101,132,015
-1 101,132,015
Keep dividing by the next highest number until you cannot divide anymore.

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

15472353371,2771,6856,38515,83960,01979,195300,095430,3492,151,74520,226,403101,132,015
-1-5-47-235-337-1,277-1,685-6,385-15,839-60,019-79,195-300,095-430,349-2,151,745-20,226,403-101,132,015

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