Q: What are the factor combinations of the number 135,321,210?

 A:
Positive:   1 x 1353212102 x 676606053 x 451070705 x 270642426 x 225535359 x 1503569010 x 1353212115 x 902141418 x 751784530 x 451070737 x 365733045 x 300713874 x 182866590 x 1503569111 x 1219110185 x 731466222 x 609555333 x 406370370 x 365733555 x 243822666 x 2031851110 x 1219111665 x 812743330 x 40637
Negative: -1 x -135321210-2 x -67660605-3 x -45107070-5 x -27064242-6 x -22553535-9 x -15035690-10 x -13532121-15 x -9021414-18 x -7517845-30 x -4510707-37 x -3657330-45 x -3007138-74 x -1828665-90 x -1503569-111 x -1219110-185 x -731466-222 x -609555-333 x -406370-370 x -365733-555 x -243822-666 x -203185-1110 x -121911-1665 x -81274-3330 x -40637


How do I find the factor combinations of the number 135,321,210?

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 135,321,210, 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.

1 135,321,210
-1 -135,321,210

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 135,321,210.

Example:
1 x 135,321,210 = 135,321,210
and
-1 x -135,321,210 = 135,321,210
Notice both answers equal 135,321,210

With that explanation out of the way, let's continue. Next, we take the number 135,321,210 and divide it by 2:

135,321,210 ÷ 2 = 67,660,605

If the quotient is a whole number, then 2 and 67,660,605 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 67,660,605 135,321,210
-1 -2 -67,660,605 -135,321,210

Now, we try dividing 135,321,210 by 3:

135,321,210 ÷ 3 = 45,107,070

If the quotient is a whole number, then 3 and 45,107,070 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 45,107,070 67,660,605 135,321,210
-1 -2 -3 -45,107,070 -67,660,605 -135,321,210

Let's try dividing by 4:

135,321,210 ÷ 4 = 33,830,302.5

If the quotient is a whole number, then 4 and 33,830,302.5 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 45,107,070 67,660,605 135,321,210
-1 -2 -3 -45,107,070 -67,660,605 135,321,210
Keep dividing by the next highest number until you cannot divide anymore.

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

12356910151830374574901111852223333705556661,1101,6653,33040,63781,274121,911203,185243,822365,733406,370609,555731,4661,219,1101,503,5691,828,6653,007,1383,657,3304,510,7077,517,8459,021,41413,532,12115,035,69022,553,53527,064,24245,107,07067,660,605135,321,210
-1-2-3-5-6-9-10-15-18-30-37-45-74-90-111-185-222-333-370-555-666-1,110-1,665-3,330-40,637-81,274-121,911-203,185-243,822-365,733-406,370-609,555-731,466-1,219,110-1,503,569-1,828,665-3,007,138-3,657,330-4,510,707-7,517,845-9,021,414-13,532,121-15,035,690-22,553,535-27,064,242-45,107,070-67,660,605-135,321,210

More Examples

Here are some more numbers to try:

135,321,208135,321,209135,321,211135,321,212
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