Q: What are the factor combinations of the number 121,531,007?

 A:
Positive:   1 x 12153100713 x 934853983 x 1464229163 x 745589691 x 1758771079 x 1126332119 x 573538983 x 13529
Negative: -1 x -121531007-13 x -9348539-83 x -1464229-163 x -745589-691 x -175877-1079 x -112633-2119 x -57353-8983 x -13529


How do I find the factor combinations of the number 121,531,007?

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 121,531,007, 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.

1 121,531,007
-1 -121,531,007

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 121,531,007.

Example:
1 x 121,531,007 = 121,531,007
and
-1 x -121,531,007 = 121,531,007
Notice both answers equal 121,531,007

With that explanation out of the way, let's continue. Next, we take the number 121,531,007 and divide it by 2:

121,531,007 ÷ 2 = 60,765,503.5

If the quotient is a whole number, then 2 and 60,765,503.5 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:

1 121,531,007
-1 -121,531,007

Now, we try dividing 121,531,007 by 3:

121,531,007 ÷ 3 = 40,510,335.6667

If the quotient is a whole number, then 3 and 40,510,335.6667 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:

1 121,531,007
-1 -121,531,007

Let's try dividing by 4:

121,531,007 ÷ 4 = 30,382,751.75

If the quotient is a whole number, then 4 and 30,382,751.75 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:

1 121,531,007
-1 121,531,007
Keep dividing by the next highest number until you cannot divide anymore.

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

113831636911,0792,1198,98313,52957,353112,633175,877745,5891,464,2299,348,539121,531,007
-1-13-83-163-691-1,079-2,119-8,983-13,529-57,353-112,633-175,877-745,589-1,464,229-9,348,539-121,531,007

More Examples

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