Q: What are the factor combinations of the number 31,628,908?

 A:
Positive:   1 x 316289082 x 158144544 x 790722717 x 186052429 x 109065234 x 93026243 x 73555658 x 54532668 x 46513186 x 367778116 x 272663172 x 183889373 x 84796493 x 64156731 x 43268746 x 42398986 x 320781247 x 253641462 x 216341492 x 211991972 x 160392494 x 126822924 x 108174988 x 6341
Negative: -1 x -31628908-2 x -15814454-4 x -7907227-17 x -1860524-29 x -1090652-34 x -930262-43 x -735556-58 x -545326-68 x -465131-86 x -367778-116 x -272663-172 x -183889-373 x -84796-493 x -64156-731 x -43268-746 x -42398-986 x -32078-1247 x -25364-1462 x -21634-1492 x -21199-1972 x -16039-2494 x -12682-2924 x -10817-4988 x -6341


How do I find the factor combinations of the number 31,628,908?

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 31,628,908, 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 31,628,908
-1 -31,628,908

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 31,628,908.

Example:
1 x 31,628,908 = 31,628,908
and
-1 x -31,628,908 = 31,628,908
Notice both answers equal 31,628,908

With that explanation out of the way, let's continue. Next, we take the number 31,628,908 and divide it by 2:

31,628,908 ÷ 2 = 15,814,454

If the quotient is a whole number, then 2 and 15,814,454 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 15,814,454 31,628,908
-1 -2 -15,814,454 -31,628,908

Now, we try dividing 31,628,908 by 3:

31,628,908 ÷ 3 = 10,542,969.3333

If the quotient is a whole number, then 3 and 10,542,969.3333 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 2 15,814,454 31,628,908
-1 -2 -15,814,454 -31,628,908

Let's try dividing by 4:

31,628,908 ÷ 4 = 7,907,227

If the quotient is a whole number, then 4 and 7,907,227 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 4 7,907,227 15,814,454 31,628,908
-1 -2 -4 -7,907,227 -15,814,454 31,628,908
Keep dividing by the next highest number until you cannot divide anymore.

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

124172934435868861161723734937317469861,2471,4621,4921,9722,4942,9244,9886,34110,81712,68216,03921,19921,63425,36432,07842,39843,26864,15684,796183,889272,663367,778465,131545,326735,556930,2621,090,6521,860,5247,907,22715,814,45431,628,908
-1-2-4-17-29-34-43-58-68-86-116-172-373-493-731-746-986-1,247-1,462-1,492-1,972-2,494-2,924-4,988-6,341-10,817-12,682-16,039-21,199-21,634-25,364-32,078-42,398-43,268-64,156-84,796-183,889-272,663-367,778-465,131-545,326-735,556-930,262-1,090,652-1,860,524-7,907,227-15,814,454-31,628,908

More Examples

Here are some more numbers to try:

31,628,90631,628,90731,628,90931,628,910
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