Q: What are the factor combinations of the number 314,421,425?

 A:
Positive:   1 x 3144214255 x 6288428525 x 1257685789 x 3532825251 x 1252675445 x 706565563 x 5584751255 x 2505352225 x 1413132815 x 1116956275 x 5010714075 x 22339
Negative: -1 x -314421425-5 x -62884285-25 x -12576857-89 x -3532825-251 x -1252675-445 x -706565-563 x -558475-1255 x -250535-2225 x -141313-2815 x -111695-6275 x -50107-14075 x -22339


How do I find the factor combinations of the number 314,421,425?

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 314,421,425, 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.

1 314,421,425
-1 -314,421,425

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 314,421,425.

Example:
1 x 314,421,425 = 314,421,425
and
-1 x -314,421,425 = 314,421,425
Notice both answers equal 314,421,425

With that explanation out of the way, let's continue. Next, we take the number 314,421,425 and divide it by 2:

314,421,425 ÷ 2 = 157,210,712.5

If the quotient is a whole number, then 2 and 157,210,712.5 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:

1 314,421,425
-1 -314,421,425

Now, we try dividing 314,421,425 by 3:

314,421,425 ÷ 3 = 104,807,141.6667

If the quotient is a whole number, then 3 and 104,807,141.6667 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:

1 314,421,425
-1 -314,421,425

Let's try dividing by 4:

314,421,425 ÷ 4 = 78,605,356.25

If the quotient is a whole number, then 4 and 78,605,356.25 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:

1 314,421,425
-1 314,421,425
Keep dividing by the next highest number until you cannot divide anymore.

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

1525892514455631,2552,2252,8156,27514,07522,33950,107111,695141,313250,535558,475706,5651,252,6753,532,82512,576,85762,884,285314,421,425
-1-5-25-89-251-445-563-1,255-2,225-2,815-6,275-14,075-22,339-50,107-111,695-141,313-250,535-558,475-706,565-1,252,675-3,532,825-12,576,857-62,884,285-314,421,425

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