Q: What are the factor combinations of the number 712,823,072?

 A:
Positive:   1 x 7128230722 x 3564115364 x 1782057688 x 8910288413 x 5483254416 x 4455144226 x 2741627232 x 2227572152 x 1370813689 x 8009248104 x 6854068169 x 4217888178 x 4004624208 x 3427034338 x 2108944356 x 2002312416 x 1713517676 x 1054472712 x 10011561157 x 6160961352 x 5272361424 x 5005781481 x 4813122314 x 3080482704 x 2636182848 x 2502892962 x 2406564628 x 1540245408 x 1318095924 x 1203289256 x 7701211848 x 6016415041 x 4739218512 x 3850619253 x 3702423696 x 30082
Negative: -1 x -712823072-2 x -356411536-4 x -178205768-8 x -89102884-13 x -54832544-16 x -44551442-26 x -27416272-32 x -22275721-52 x -13708136-89 x -8009248-104 x -6854068-169 x -4217888-178 x -4004624-208 x -3427034-338 x -2108944-356 x -2002312-416 x -1713517-676 x -1054472-712 x -1001156-1157 x -616096-1352 x -527236-1424 x -500578-1481 x -481312-2314 x -308048-2704 x -263618-2848 x -250289-2962 x -240656-4628 x -154024-5408 x -131809-5924 x -120328-9256 x -77012-11848 x -60164-15041 x -47392-18512 x -38506-19253 x -37024-23696 x -30082


How do I find the factor combinations of the number 712,823,072?

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 712,823,072, 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.

1 712,823,072
-1 -712,823,072

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 712,823,072.

Example:
1 x 712,823,072 = 712,823,072
and
-1 x -712,823,072 = 712,823,072
Notice both answers equal 712,823,072

With that explanation out of the way, let's continue. Next, we take the number 712,823,072 and divide it by 2:

712,823,072 ÷ 2 = 356,411,536

If the quotient is a whole number, then 2 and 356,411,536 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 2 356,411,536 712,823,072
-1 -2 -356,411,536 -712,823,072

Now, we try dividing 712,823,072 by 3:

712,823,072 ÷ 3 = 237,607,690.6667

If the quotient is a whole number, then 3 and 237,607,690.6667 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 2 356,411,536 712,823,072
-1 -2 -356,411,536 -712,823,072

Let's try dividing by 4:

712,823,072 ÷ 4 = 178,205,768

If the quotient is a whole number, then 4 and 178,205,768 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 4 178,205,768 356,411,536 712,823,072
-1 -2 -4 -178,205,768 -356,411,536 712,823,072
Keep dividing by the next highest number until you cannot divide anymore.

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

12481316263252891041691782083383564166767121,1571,3521,4241,4812,3142,7042,8482,9624,6285,4085,9249,25611,84815,04118,51219,25323,69630,08237,02438,50647,39260,16477,012120,328131,809154,024240,656250,289263,618308,048481,312500,578527,236616,0961,001,1561,054,4721,713,5172,002,3122,108,9443,427,0344,004,6244,217,8886,854,0688,009,24813,708,13622,275,72127,416,27244,551,44254,832,54489,102,884178,205,768356,411,536712,823,072
-1-2-4-8-13-16-26-32-52-89-104-169-178-208-338-356-416-676-712-1,157-1,352-1,424-1,481-2,314-2,704-2,848-2,962-4,628-5,408-5,924-9,256-11,848-15,041-18,512-19,253-23,696-30,082-37,024-38,506-47,392-60,164-77,012-120,328-131,809-154,024-240,656-250,289-263,618-308,048-481,312-500,578-527,236-616,096-1,001,156-1,054,472-1,713,517-2,002,312-2,108,944-3,427,034-4,004,624-4,217,888-6,854,068-8,009,248-13,708,136-22,275,721-27,416,272-44,551,442-54,832,544-89,102,884-178,205,768-356,411,536-712,823,072

More Examples

Here are some more numbers to try:

712,823,070712,823,071712,823,073712,823,074
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