Q: What are the factor combinations of the number 21,376,729?

 A:
Positive:   1 x 2137672911 x 194333919 x 112509123 x 929423209 x 102281253 x 84493437 x 489174447 x 4807
Negative: -1 x -21376729-11 x -1943339-19 x -1125091-23 x -929423-209 x -102281-253 x -84493-437 x -48917-4447 x -4807


How do I find the factor combinations of the number 21,376,729?

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 21,376,729, 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 21,376,729
-1 -21,376,729

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 21,376,729.

Example:
1 x 21,376,729 = 21,376,729
and
-1 x -21,376,729 = 21,376,729
Notice both answers equal 21,376,729

With that explanation out of the way, let's continue. Next, we take the number 21,376,729 and divide it by 2:

21,376,729 ÷ 2 = 10,688,364.5

If the quotient is a whole number, then 2 and 10,688,364.5 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 21,376,729
-1 -21,376,729

Now, we try dividing 21,376,729 by 3:

21,376,729 ÷ 3 = 7,125,576.3333

If the quotient is a whole number, then 3 and 7,125,576.3333 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 21,376,729
-1 -21,376,729

Let's try dividing by 4:

21,376,729 ÷ 4 = 5,344,182.25

If the quotient is a whole number, then 4 and 5,344,182.25 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 21,376,729
-1 21,376,729
Keep dividing by the next highest number until you cannot divide anymore.

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

11119232092534374,4474,80748,91784,493102,281929,4231,125,0911,943,33921,376,729
-1-11-19-23-209-253-437-4,447-4,807-48,917-84,493-102,281-929,423-1,125,091-1,943,339-21,376,729

More Examples

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