Q: What are the factor combinations of the number 21,461,635?

 A:
Positive:   1 x 214616355 x 429232713 x 165089565 x 33017973 x 293995365 x 58799949 x 226154523 x 4745
Negative: -1 x -21461635-5 x -4292327-13 x -1650895-65 x -330179-73 x -293995-365 x -58799-949 x -22615-4523 x -4745


How do I find the factor combinations of the number 21,461,635?

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 21,461,635, 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 21,461,635
-1 -21,461,635

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 21,461,635.

Example:
1 x 21,461,635 = 21,461,635
and
-1 x -21,461,635 = 21,461,635
Notice both answers equal 21,461,635

With that explanation out of the way, let's continue. Next, we take the number 21,461,635 and divide it by 2:

21,461,635 ÷ 2 = 10,730,817.5

If the quotient is a whole number, then 2 and 10,730,817.5 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 21,461,635
-1 -21,461,635

Now, we try dividing 21,461,635 by 3:

21,461,635 ÷ 3 = 7,153,878.3333

If the quotient is a whole number, then 3 and 7,153,878.3333 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 21,461,635
-1 -21,461,635

Let's try dividing by 4:

21,461,635 ÷ 4 = 5,365,408.75

If the quotient is a whole number, then 4 and 5,365,408.75 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 21,461,635
-1 21,461,635
Keep dividing by the next highest number until you cannot divide anymore.

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

151365733659494,5234,74522,61558,799293,995330,1791,650,8954,292,32721,461,635
-1-5-13-65-73-365-949-4,523-4,745-22,615-58,799-293,995-330,179-1,650,895-4,292,327-21,461,635

More Examples

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