Q: What are the factor combinations of the number 21,387,977?

 A:
Positive:   1 x 2138797713 x 164522919 x 1125683131 x 163267247 x 86591661 x 323571703 x 125592489 x 8593
Negative: -1 x -21387977-13 x -1645229-19 x -1125683-131 x -163267-247 x -86591-661 x -32357-1703 x -12559-2489 x -8593


How do I find the factor combinations of the number 21,387,977?

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 21,387,977, 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 21,387,977
-1 -21,387,977

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 21,387,977.

Example:
1 x 21,387,977 = 21,387,977
and
-1 x -21,387,977 = 21,387,977
Notice both answers equal 21,387,977

With that explanation out of the way, let's continue. Next, we take the number 21,387,977 and divide it by 2:

21,387,977 ÷ 2 = 10,693,988.5

If the quotient is a whole number, then 2 and 10,693,988.5 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 21,387,977
-1 -21,387,977

Now, we try dividing 21,387,977 by 3:

21,387,977 ÷ 3 = 7,129,325.6667

If the quotient is a whole number, then 3 and 7,129,325.6667 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 21,387,977
-1 -21,387,977

Let's try dividing by 4:

21,387,977 ÷ 4 = 5,346,994.25

If the quotient is a whole number, then 4 and 5,346,994.25 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 21,387,977
-1 21,387,977
Keep dividing by the next highest number until you cannot divide anymore.

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

113191312476611,7032,4898,59312,55932,35786,591163,2671,125,6831,645,22921,387,977
-1-13-19-131-247-661-1,703-2,489-8,593-12,559-32,357-86,591-163,267-1,125,683-1,645,229-21,387,977

More Examples

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