Q: What are the factor combinations of the number 72,131,675?

 A:
Positive:   1 x 721316755 x 144263357 x 1030452511 x 655742525 x 288526735 x 206090549 x 147207553 x 136097555 x 131148577 x 936775101 x 714175175 x 412181245 x 294415265 x 272195275 x 262297371 x 194425385 x 187355505 x 142835539 x 133825583 x 123725707 x 1020251111 x 649251225 x 588831325 x 544391855 x 388851925 x 374712525 x 285672597 x 277752695 x 267652915 x 247453535 x 204054081 x 176754949 x 145755353 x 134755555 x 129857777 x 9275
Negative: -1 x -72131675-5 x -14426335-7 x -10304525-11 x -6557425-25 x -2885267-35 x -2060905-49 x -1472075-53 x -1360975-55 x -1311485-77 x -936775-101 x -714175-175 x -412181-245 x -294415-265 x -272195-275 x -262297-371 x -194425-385 x -187355-505 x -142835-539 x -133825-583 x -123725-707 x -102025-1111 x -64925-1225 x -58883-1325 x -54439-1855 x -38885-1925 x -37471-2525 x -28567-2597 x -27775-2695 x -26765-2915 x -24745-3535 x -20405-4081 x -17675-4949 x -14575-5353 x -13475-5555 x -12985-7777 x -9275


How do I find the factor combinations of the number 72,131,675?

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 72,131,675, 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 72,131,675
-1 -72,131,675

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 72,131,675.

Example:
1 x 72,131,675 = 72,131,675
and
-1 x -72,131,675 = 72,131,675
Notice both answers equal 72,131,675

With that explanation out of the way, let's continue. Next, we take the number 72,131,675 and divide it by 2:

72,131,675 ÷ 2 = 36,065,837.5

If the quotient is a whole number, then 2 and 36,065,837.5 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 72,131,675
-1 -72,131,675

Now, we try dividing 72,131,675 by 3:

72,131,675 ÷ 3 = 24,043,891.6667

If the quotient is a whole number, then 3 and 24,043,891.6667 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 72,131,675
-1 -72,131,675

Let's try dividing by 4:

72,131,675 ÷ 4 = 18,032,918.75

If the quotient is a whole number, then 4 and 18,032,918.75 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 72,131,675
-1 72,131,675
Keep dividing by the next highest number until you cannot divide anymore.

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

157112535495355771011752452652753713855055395837071,1111,2251,3251,8551,9252,5252,5972,6952,9153,5354,0814,9495,3535,5557,7779,27512,98513,47514,57517,67520,40524,74526,76527,77528,56737,47138,88554,43958,88364,925102,025123,725133,825142,835187,355194,425262,297272,195294,415412,181714,175936,7751,311,4851,360,9751,472,0752,060,9052,885,2676,557,42510,304,52514,426,33572,131,675
-1-5-7-11-25-35-49-53-55-77-101-175-245-265-275-371-385-505-539-583-707-1,111-1,225-1,325-1,855-1,925-2,525-2,597-2,695-2,915-3,535-4,081-4,949-5,353-5,555-7,777-9,275-12,985-13,475-14,575-17,675-20,405-24,745-26,765-27,775-28,567-37,471-38,885-54,439-58,883-64,925-102,025-123,725-133,825-142,835-187,355-194,425-262,297-272,195-294,415-412,181-714,175-936,775-1,311,485-1,360,975-1,472,075-2,060,905-2,885,267-6,557,425-10,304,525-14,426,335-72,131,675

More Examples

Here are some more numbers to try:

72,131,67372,131,67472,131,67672,131,677
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