Q: What are the factor combinations of the number 140,114,221?

 A:
Positive:   1 x 14011422113 x 1077801717 x 8242013221 x 634001431 x 3250911471 x 952515603 x 250077327 x 19123
Negative: -1 x -140114221-13 x -10778017-17 x -8242013-221 x -634001-431 x -325091-1471 x -95251-5603 x -25007-7327 x -19123


How do I find the factor combinations of the number 140,114,221?

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 140,114,221, 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.

1 140,114,221
-1 -140,114,221

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 140,114,221.

Example:
1 x 140,114,221 = 140,114,221
and
-1 x -140,114,221 = 140,114,221
Notice both answers equal 140,114,221

With that explanation out of the way, let's continue. Next, we take the number 140,114,221 and divide it by 2:

140,114,221 ÷ 2 = 70,057,110.5

If the quotient is a whole number, then 2 and 70,057,110.5 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:

1 140,114,221
-1 -140,114,221

Now, we try dividing 140,114,221 by 3:

140,114,221 ÷ 3 = 46,704,740.3333

If the quotient is a whole number, then 3 and 46,704,740.3333 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:

1 140,114,221
-1 -140,114,221

Let's try dividing by 4:

140,114,221 ÷ 4 = 35,028,555.25

If the quotient is a whole number, then 4 and 35,028,555.25 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:

1 140,114,221
-1 140,114,221
Keep dividing by the next highest number until you cannot divide anymore.

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

113172214311,4715,6037,32719,12325,00795,251325,091634,0018,242,01310,778,017140,114,221
-1-13-17-221-431-1,471-5,603-7,327-19,123-25,007-95,251-325,091-634,001-8,242,013-10,778,017-140,114,221

More Examples

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