Q: What are the factor combinations of the number 21,462,365?

 A:
Positive:   1 x 214623655 x 429247373 x 294005127 x 168995365 x 58801463 x 46355635 x 337992315 x 9271
Negative: -1 x -21462365-5 x -4292473-73 x -294005-127 x -168995-365 x -58801-463 x -46355-635 x -33799-2315 x -9271


How do I find the factor combinations of the number 21,462,365?

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 21,462,365, 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 21,462,365
-1 -21,462,365

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 21,462,365.

Example:
1 x 21,462,365 = 21,462,365
and
-1 x -21,462,365 = 21,462,365
Notice both answers equal 21,462,365

With that explanation out of the way, let's continue. Next, we take the number 21,462,365 and divide it by 2:

21,462,365 ÷ 2 = 10,731,182.5

If the quotient is a whole number, then 2 and 10,731,182.5 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 21,462,365
-1 -21,462,365

Now, we try dividing 21,462,365 by 3:

21,462,365 ÷ 3 = 7,154,121.6667

If the quotient is a whole number, then 3 and 7,154,121.6667 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 21,462,365
-1 -21,462,365

Let's try dividing by 4:

21,462,365 ÷ 4 = 5,365,591.25

If the quotient is a whole number, then 4 and 5,365,591.25 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 21,462,365
-1 21,462,365
Keep dividing by the next highest number until you cannot divide anymore.

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

15731273654636352,3159,27133,79946,35558,801168,995294,0054,292,47321,462,365
-1-5-73-127-365-463-635-2,315-9,271-33,799-46,355-58,801-168,995-294,005-4,292,473-21,462,365

More Examples

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