Q: What are the factor combinations of the number 21,546,725?

 A:
Positive:   1 x 215467255 x 430934525 x 86186961 x 35322571 x 303475199 x 108275305 x 70645355 x 60695995 x 216551525 x 141291775 x 121394331 x 4975
Negative: -1 x -21546725-5 x -4309345-25 x -861869-61 x -353225-71 x -303475-199 x -108275-305 x -70645-355 x -60695-995 x -21655-1525 x -14129-1775 x -12139-4331 x -4975


How do I find the factor combinations of the number 21,546,725?

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 21,546,725, 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 21,546,725
-1 -21,546,725

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 21,546,725.

Example:
1 x 21,546,725 = 21,546,725
and
-1 x -21,546,725 = 21,546,725
Notice both answers equal 21,546,725

With that explanation out of the way, let's continue. Next, we take the number 21,546,725 and divide it by 2:

21,546,725 ÷ 2 = 10,773,362.5

If the quotient is a whole number, then 2 and 10,773,362.5 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 21,546,725
-1 -21,546,725

Now, we try dividing 21,546,725 by 3:

21,546,725 ÷ 3 = 7,182,241.6667

If the quotient is a whole number, then 3 and 7,182,241.6667 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 21,546,725
-1 -21,546,725

Let's try dividing by 4:

21,546,725 ÷ 4 = 5,386,681.25

If the quotient is a whole number, then 4 and 5,386,681.25 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 21,546,725
-1 21,546,725
Keep dividing by the next highest number until you cannot divide anymore.

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

152561711993053559951,5251,7754,3314,97512,13914,12921,65560,69570,645108,275303,475353,225861,8694,309,34521,546,725
-1-5-25-61-71-199-305-355-995-1,525-1,775-4,331-4,975-12,139-14,129-21,655-60,695-70,645-108,275-303,475-353,225-861,869-4,309,345-21,546,725

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