Q: What are the factor combinations of the number 312,323,340?

 A:
Positive:   1 x 3123233402 x 1561616703 x 1041077804 x 780808355 x 624646686 x 520538907 x 4461762010 x 3123233412 x 2602694514 x 2230881015 x 2082155620 x 1561616721 x 1487254028 x 1115440530 x 1041077835 x 892352442 x 743627060 x 520538970 x 446176279 x 395346084 x 3718135105 x 2974508140 x 2230881158 x 1976730210 x 1487254237 x 1317820316 x 988365395 x 790692420 x 743627474 x 658910553 x 564780790 x 395346948 x 3294551106 x 2823901185 x 2635641580 x 1976731659 x 1882602212 x 1411952370 x 1317822765 x 1129563318 x 941304740 x 658915530 x 564786636 x 470658295 x 376529413 x 3318011060 x 2823916590 x 18826
Negative: -1 x -312323340-2 x -156161670-3 x -104107780-4 x -78080835-5 x -62464668-6 x -52053890-7 x -44617620-10 x -31232334-12 x -26026945-14 x -22308810-15 x -20821556-20 x -15616167-21 x -14872540-28 x -11154405-30 x -10410778-35 x -8923524-42 x -7436270-60 x -5205389-70 x -4461762-79 x -3953460-84 x -3718135-105 x -2974508-140 x -2230881-158 x -1976730-210 x -1487254-237 x -1317820-316 x -988365-395 x -790692-420 x -743627-474 x -658910-553 x -564780-790 x -395346-948 x -329455-1106 x -282390-1185 x -263564-1580 x -197673-1659 x -188260-2212 x -141195-2370 x -131782-2765 x -112956-3318 x -94130-4740 x -65891-5530 x -56478-6636 x -47065-8295 x -37652-9413 x -33180-11060 x -28239-16590 x -18826


How do I find the factor combinations of the number 312,323,340?

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 312,323,340, 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.

1 312,323,340
-1 -312,323,340

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 312,323,340.

Example:
1 x 312,323,340 = 312,323,340
and
-1 x -312,323,340 = 312,323,340
Notice both answers equal 312,323,340

With that explanation out of the way, let's continue. Next, we take the number 312,323,340 and divide it by 2:

312,323,340 ÷ 2 = 156,161,670

If the quotient is a whole number, then 2 and 156,161,670 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 2 156,161,670 312,323,340
-1 -2 -156,161,670 -312,323,340

Now, we try dividing 312,323,340 by 3:

312,323,340 ÷ 3 = 104,107,780

If the quotient is a whole number, then 3 and 104,107,780 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 3 104,107,780 156,161,670 312,323,340
-1 -2 -3 -104,107,780 -156,161,670 -312,323,340

Let's try dividing by 4:

312,323,340 ÷ 4 = 78,080,835

If the quotient is a whole number, then 4 and 78,080,835 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 78,080,835 104,107,780 156,161,670 312,323,340
-1 -2 -3 -4 -78,080,835 -104,107,780 -156,161,670 312,323,340
Keep dividing by the next highest number until you cannot divide anymore.

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

123456710121415202128303542607079841051401582102373163954204745537909481,1061,1851,5801,6592,2122,3702,7653,3184,7405,5306,6368,2959,41311,06016,59018,82628,23933,18037,65247,06556,47865,89194,130112,956131,782141,195188,260197,673263,564282,390329,455395,346564,780658,910743,627790,692988,3651,317,8201,487,2541,976,7302,230,8812,974,5083,718,1353,953,4604,461,7625,205,3897,436,2708,923,52410,410,77811,154,40514,872,54015,616,16720,821,55622,308,81026,026,94531,232,33444,617,62052,053,89062,464,66878,080,835104,107,780156,161,670312,323,340
-1-2-3-4-5-6-7-10-12-14-15-20-21-28-30-35-42-60-70-79-84-105-140-158-210-237-316-395-420-474-553-790-948-1,106-1,185-1,580-1,659-2,212-2,370-2,765-3,318-4,740-5,530-6,636-8,295-9,413-11,060-16,590-18,826-28,239-33,180-37,652-47,065-56,478-65,891-94,130-112,956-131,782-141,195-188,260-197,673-263,564-282,390-329,455-395,346-564,780-658,910-743,627-790,692-988,365-1,317,820-1,487,254-1,976,730-2,230,881-2,974,508-3,718,135-3,953,460-4,461,762-5,205,389-7,436,270-8,923,524-10,410,778-11,154,405-14,872,540-15,616,167-20,821,556-22,308,810-26,026,945-31,232,334-44,617,620-52,053,890-62,464,668-78,080,835-104,107,780-156,161,670-312,323,340

More Examples

Here are some more numbers to try:

312,323,338312,323,339312,323,341312,323,342
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