Q: What are the factor combinations of the number 21,523,445?

 A:
Positive:   1 x 215234455 x 430468917 x 126608585 x 253217313 x 68765809 x 266051565 x 137534045 x 5321
Negative: -1 x -21523445-5 x -4304689-17 x -1266085-85 x -253217-313 x -68765-809 x -26605-1565 x -13753-4045 x -5321


How do I find the factor combinations of the number 21,523,445?

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 21,523,445, 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 21,523,445
-1 -21,523,445

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 21,523,445.

Example:
1 x 21,523,445 = 21,523,445
and
-1 x -21,523,445 = 21,523,445
Notice both answers equal 21,523,445

With that explanation out of the way, let's continue. Next, we take the number 21,523,445 and divide it by 2:

21,523,445 ÷ 2 = 10,761,722.5

If the quotient is a whole number, then 2 and 10,761,722.5 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 21,523,445
-1 -21,523,445

Now, we try dividing 21,523,445 by 3:

21,523,445 ÷ 3 = 7,174,481.6667

If the quotient is a whole number, then 3 and 7,174,481.6667 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 21,523,445
-1 -21,523,445

Let's try dividing by 4:

21,523,445 ÷ 4 = 5,380,861.25

If the quotient is a whole number, then 4 and 5,380,861.25 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 21,523,445
-1 21,523,445
Keep dividing by the next highest number until you cannot divide anymore.

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

1517853138091,5654,0455,32113,75326,60568,765253,2171,266,0854,304,68921,523,445
-1-5-17-85-313-809-1,565-4,045-5,321-13,753-26,605-68,765-253,217-1,266,085-4,304,689-21,523,445

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