Q: What are the factor combinations of the number 712,116,378?

 A:
Positive:   1 x 7121163782 x 3560581893 x 2373721266 x 1186860639 x 7912404218 x 3956202143 x 1656084686 x 8280423129 x 5520282191 x 3728358258 x 2760141382 x 1864179387 x 1840094573 x 1242786774 x 9200471146 x 6213931719 x 4142623438 x 2071314817 x 1478348213 x 867069634 x 7391714451 x 4927816426 x 4335324639 x 28902
Negative: -1 x -712116378-2 x -356058189-3 x -237372126-6 x -118686063-9 x -79124042-18 x -39562021-43 x -16560846-86 x -8280423-129 x -5520282-191 x -3728358-258 x -2760141-382 x -1864179-387 x -1840094-573 x -1242786-774 x -920047-1146 x -621393-1719 x -414262-3438 x -207131-4817 x -147834-8213 x -86706-9634 x -73917-14451 x -49278-16426 x -43353-24639 x -28902


How do I find the factor combinations of the number 712,116,378?

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 712,116,378, 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.

1 712,116,378
-1 -712,116,378

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 712,116,378.

Example:
1 x 712,116,378 = 712,116,378
and
-1 x -712,116,378 = 712,116,378
Notice both answers equal 712,116,378

With that explanation out of the way, let's continue. Next, we take the number 712,116,378 and divide it by 2:

712,116,378 ÷ 2 = 356,058,189

If the quotient is a whole number, then 2 and 356,058,189 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 2 356,058,189 712,116,378
-1 -2 -356,058,189 -712,116,378

Now, we try dividing 712,116,378 by 3:

712,116,378 ÷ 3 = 237,372,126

If the quotient is a whole number, then 3 and 237,372,126 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 3 237,372,126 356,058,189 712,116,378
-1 -2 -3 -237,372,126 -356,058,189 -712,116,378

Let's try dividing by 4:

712,116,378 ÷ 4 = 178,029,094.5

If the quotient is a whole number, then 4 and 178,029,094.5 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 2 3 237,372,126 356,058,189 712,116,378
-1 -2 -3 -237,372,126 -356,058,189 712,116,378
Keep dividing by the next highest number until you cannot divide anymore.

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

123691843861291912583823875737741,1461,7193,4384,8178,2139,63414,45116,42624,63928,90243,35349,27873,91786,706147,834207,131414,262621,393920,0471,242,7861,840,0941,864,1792,760,1413,728,3585,520,2828,280,42316,560,84639,562,02179,124,042118,686,063237,372,126356,058,189712,116,378
-1-2-3-6-9-18-43-86-129-191-258-382-387-573-774-1,146-1,719-3,438-4,817-8,213-9,634-14,451-16,426-24,639-28,902-43,353-49,278-73,917-86,706-147,834-207,131-414,262-621,393-920,047-1,242,786-1,840,094-1,864,179-2,760,141-3,728,358-5,520,282-8,280,423-16,560,846-39,562,021-79,124,042-118,686,063-237,372,126-356,058,189-712,116,378

More Examples

Here are some more numbers to try:

712,116,376712,116,377712,116,379712,116,380
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