Q: What are the factor combinations of the number 688,376,220?

 A:
Positive:   1 x 6883762202 x 3441881103 x 2294587404 x 1720940555 x 1376752446 x 1147293707 x 9833946010 x 6883762212 x 5736468514 x 4916973015 x 4589174820 x 3441881121 x 3277982028 x 2458486530 x 2294587435 x 1966789242 x 1638991060 x 1147293770 x 983394684 x 8194955105 x 6555964140 x 4916973210 x 3277982420 x 1638991
Negative: -1 x -688376220-2 x -344188110-3 x -229458740-4 x -172094055-5 x -137675244-6 x -114729370-7 x -98339460-10 x -68837622-12 x -57364685-14 x -49169730-15 x -45891748-20 x -34418811-21 x -32779820-28 x -24584865-30 x -22945874-35 x -19667892-42 x -16389910-60 x -11472937-70 x -9833946-84 x -8194955-105 x -6555964-140 x -4916973-210 x -3277982-420 x -1638991


How do I find the factor combinations of the number 688,376,220?

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 688,376,220, 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.

1 688,376,220
-1 -688,376,220

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 688,376,220.

Example:
1 x 688,376,220 = 688,376,220
and
-1 x -688,376,220 = 688,376,220
Notice both answers equal 688,376,220

With that explanation out of the way, let's continue. Next, we take the number 688,376,220 and divide it by 2:

688,376,220 ÷ 2 = 344,188,110

If the quotient is a whole number, then 2 and 344,188,110 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 2 344,188,110 688,376,220
-1 -2 -344,188,110 -688,376,220

Now, we try dividing 688,376,220 by 3:

688,376,220 ÷ 3 = 229,458,740

If the quotient is a whole number, then 3 and 229,458,740 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 3 229,458,740 344,188,110 688,376,220
-1 -2 -3 -229,458,740 -344,188,110 -688,376,220

Let's try dividing by 4:

688,376,220 ÷ 4 = 172,094,055

If the quotient is a whole number, then 4 and 172,094,055 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 4 172,094,055 229,458,740 344,188,110 688,376,220
-1 -2 -3 -4 -172,094,055 -229,458,740 -344,188,110 688,376,220
Keep dividing by the next highest number until you cannot divide anymore.

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

1234567101214152021283035426070841051402104201,638,9913,277,9824,916,9736,555,9648,194,9559,833,94611,472,93716,389,91019,667,89222,945,87424,584,86532,779,82034,418,81145,891,74849,169,73057,364,68568,837,62298,339,460114,729,370137,675,244172,094,055229,458,740344,188,110688,376,220
-1-2-3-4-5-6-7-10-12-14-15-20-21-28-30-35-42-60-70-84-105-140-210-420-1,638,991-3,277,982-4,916,973-6,555,964-8,194,955-9,833,946-11,472,937-16,389,910-19,667,892-22,945,874-24,584,865-32,779,820-34,418,811-45,891,748-49,169,730-57,364,685-68,837,622-98,339,460-114,729,370-137,675,244-172,094,055-229,458,740-344,188,110-688,376,220

More Examples

Here are some more numbers to try:

688,376,218688,376,219688,376,221688,376,222
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