Q: What are the factor combinations of the number 72,420,168?

 A:
Positive:   1 x 724201682 x 362100843 x 241400564 x 181050426 x 120700288 x 905252112 x 603501424 x 3017507107 x 676824214 x 338412321 x 225608428 x 169206642 x 112804856 x 846031284 x 564022568 x 28201
Negative: -1 x -72420168-2 x -36210084-3 x -24140056-4 x -18105042-6 x -12070028-8 x -9052521-12 x -6035014-24 x -3017507-107 x -676824-214 x -338412-321 x -225608-428 x -169206-642 x -112804-856 x -84603-1284 x -56402-2568 x -28201


How do I find the factor combinations of the number 72,420,168?

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 72,420,168, 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 72,420,168
-1 -72,420,168

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 72,420,168.

Example:
1 x 72,420,168 = 72,420,168
and
-1 x -72,420,168 = 72,420,168
Notice both answers equal 72,420,168

With that explanation out of the way, let's continue. Next, we take the number 72,420,168 and divide it by 2:

72,420,168 ÷ 2 = 36,210,084

If the quotient is a whole number, then 2 and 36,210,084 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 36,210,084 72,420,168
-1 -2 -36,210,084 -72,420,168

Now, we try dividing 72,420,168 by 3:

72,420,168 ÷ 3 = 24,140,056

If the quotient is a whole number, then 3 and 24,140,056 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 24,140,056 36,210,084 72,420,168
-1 -2 -3 -24,140,056 -36,210,084 -72,420,168

Let's try dividing by 4:

72,420,168 ÷ 4 = 18,105,042

If the quotient is a whole number, then 4 and 18,105,042 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 18,105,042 24,140,056 36,210,084 72,420,168
-1 -2 -3 -4 -18,105,042 -24,140,056 -36,210,084 72,420,168
Keep dividing by the next highest number until you cannot divide anymore.

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

12346812241072143214286428561,2842,56828,20156,40284,603112,804169,206225,608338,412676,8243,017,5076,035,0149,052,52112,070,02818,105,04224,140,05636,210,08472,420,168
-1-2-3-4-6-8-12-24-107-214-321-428-642-856-1,284-2,568-28,201-56,402-84,603-112,804-169,206-225,608-338,412-676,824-3,017,507-6,035,014-9,052,521-12,070,028-18,105,042-24,140,056-36,210,084-72,420,168

More Examples

Here are some more numbers to try:

72,420,16672,420,16772,420,16972,420,170
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