Q: What are the factor combinations of the number 12,638,160?

 A:
Positive:   1 x 126381602 x 63190803 x 42127204 x 31595405 x 25276326 x 21063608 x 15797709 x 140424010 x 126381612 x 105318015 x 84254416 x 78988518 x 70212020 x 63190824 x 52659027 x 46808030 x 42127236 x 35106040 x 31595445 x 28084848 x 26329554 x 23404060 x 21063672 x 17553080 x 15797790 x 140424108 x 117020120 x 105318135 x 93616144 x 87765180 x 70212216 x 58510240 x 52659270 x 46808360 x 35106432 x 29255540 x 23404720 x 175531080 x 117022160 x 5851
Negative: -1 x -12638160-2 x -6319080-3 x -4212720-4 x -3159540-5 x -2527632-6 x -2106360-8 x -1579770-9 x -1404240-10 x -1263816-12 x -1053180-15 x -842544-16 x -789885-18 x -702120-20 x -631908-24 x -526590-27 x -468080-30 x -421272-36 x -351060-40 x -315954-45 x -280848-48 x -263295-54 x -234040-60 x -210636-72 x -175530-80 x -157977-90 x -140424-108 x -117020-120 x -105318-135 x -93616-144 x -87765-180 x -70212-216 x -58510-240 x -52659-270 x -46808-360 x -35106-432 x -29255-540 x -23404-720 x -17553-1080 x -11702-2160 x -5851


How do I find the factor combinations of the number 12,638,160?

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 12,638,160, 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 12,638,160
-1 -12,638,160

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 12,638,160.

Example:
1 x 12,638,160 = 12,638,160
and
-1 x -12,638,160 = 12,638,160
Notice both answers equal 12,638,160

With that explanation out of the way, let's continue. Next, we take the number 12,638,160 and divide it by 2:

12,638,160 ÷ 2 = 6,319,080

If the quotient is a whole number, then 2 and 6,319,080 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 6,319,080 12,638,160
-1 -2 -6,319,080 -12,638,160

Now, we try dividing 12,638,160 by 3:

12,638,160 ÷ 3 = 4,212,720

If the quotient is a whole number, then 3 and 4,212,720 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 4,212,720 6,319,080 12,638,160
-1 -2 -3 -4,212,720 -6,319,080 -12,638,160

Let's try dividing by 4:

12,638,160 ÷ 4 = 3,159,540

If the quotient is a whole number, then 4 and 3,159,540 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 3,159,540 4,212,720 6,319,080 12,638,160
-1 -2 -3 -4 -3,159,540 -4,212,720 -6,319,080 12,638,160
Keep dividing by the next highest number until you cannot divide anymore.

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

123456891012151618202427303640454854607280901081201351441802162402703604325407201,0802,1605,85111,70217,55323,40429,25535,10646,80852,65958,51070,21287,76593,616105,318117,020140,424157,977175,530210,636234,040263,295280,848315,954351,060421,272468,080526,590631,908702,120789,885842,5441,053,1801,263,8161,404,2401,579,7702,106,3602,527,6323,159,5404,212,7206,319,08012,638,160
-1-2-3-4-5-6-8-9-10-12-15-16-18-20-24-27-30-36-40-45-48-54-60-72-80-90-108-120-135-144-180-216-240-270-360-432-540-720-1,080-2,160-5,851-11,702-17,553-23,404-29,255-35,106-46,808-52,659-58,510-70,212-87,765-93,616-105,318-117,020-140,424-157,977-175,530-210,636-234,040-263,295-280,848-315,954-351,060-421,272-468,080-526,590-631,908-702,120-789,885-842,544-1,053,180-1,263,816-1,404,240-1,579,770-2,106,360-2,527,632-3,159,540-4,212,720-6,319,080-12,638,160

More Examples

Here are some more numbers to try:

12,638,15812,638,15912,638,16112,638,162
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