Q: What are the factor combinations of the number 315,150,030?

 A:
Positive:   1 x 3151500302 x 1575750153 x 1050500105 x 630300066 x 525250059 x 3501667010 x 3151500313 x 2424231015 x 2101000218 x 1750833526 x 1212115530 x 1050500131 x 1016613039 x 808077045 x 700333462 x 508306565 x 484846278 x 404038590 x 350166793 x 3388710117 x 2693590130 x 2424231155 x 2033226186 x 1694355195 x 1616154234 x 1346795279 x 1129570310 x 1016613390 x 808077403 x 782010465 x 677742558 x 564785585 x 538718806 x 391005930 x 3388711170 x 2693591209 x 2606701395 x 2259142015 x 1564022418 x 1303352790 x 1129573627 x 868904030 x 782016045 x 521347254 x 434458689 x 3627012090 x 2606717378 x 18135
Negative: -1 x -315150030-2 x -157575015-3 x -105050010-5 x -63030006-6 x -52525005-9 x -35016670-10 x -31515003-13 x -24242310-15 x -21010002-18 x -17508335-26 x -12121155-30 x -10505001-31 x -10166130-39 x -8080770-45 x -7003334-62 x -5083065-65 x -4848462-78 x -4040385-90 x -3501667-93 x -3388710-117 x -2693590-130 x -2424231-155 x -2033226-186 x -1694355-195 x -1616154-234 x -1346795-279 x -1129570-310 x -1016613-390 x -808077-403 x -782010-465 x -677742-558 x -564785-585 x -538718-806 x -391005-930 x -338871-1170 x -269359-1209 x -260670-1395 x -225914-2015 x -156402-2418 x -130335-2790 x -112957-3627 x -86890-4030 x -78201-6045 x -52134-7254 x -43445-8689 x -36270-12090 x -26067-17378 x -18135


How do I find the factor combinations of the number 315,150,030?

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 315,150,030, 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.

1 315,150,030
-1 -315,150,030

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 315,150,030.

Example:
1 x 315,150,030 = 315,150,030
and
-1 x -315,150,030 = 315,150,030
Notice both answers equal 315,150,030

With that explanation out of the way, let's continue. Next, we take the number 315,150,030 and divide it by 2:

315,150,030 ÷ 2 = 157,575,015

If the quotient is a whole number, then 2 and 157,575,015 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 2 157,575,015 315,150,030
-1 -2 -157,575,015 -315,150,030

Now, we try dividing 315,150,030 by 3:

315,150,030 ÷ 3 = 105,050,010

If the quotient is a whole number, then 3 and 105,050,010 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 3 105,050,010 157,575,015 315,150,030
-1 -2 -3 -105,050,010 -157,575,015 -315,150,030

Let's try dividing by 4:

315,150,030 ÷ 4 = 78,787,507.5

If the quotient is a whole number, then 4 and 78,787,507.5 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 3 105,050,010 157,575,015 315,150,030
-1 -2 -3 -105,050,010 -157,575,015 315,150,030
Keep dividing by the next highest number until you cannot divide anymore.

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

12356910131518263031394562657890931171301551861952342793103904034655585858069301,1701,2091,3952,0152,4182,7903,6274,0306,0457,2548,68912,09017,37818,13526,06736,27043,44552,13478,20186,890112,957130,335156,402225,914260,670269,359338,871391,005538,718564,785677,742782,010808,0771,016,6131,129,5701,346,7951,616,1541,694,3552,033,2262,424,2312,693,5903,388,7103,501,6674,040,3854,848,4625,083,0657,003,3348,080,77010,166,13010,505,00112,121,15517,508,33521,010,00224,242,31031,515,00335,016,67052,525,00563,030,006105,050,010157,575,015315,150,030
-1-2-3-5-6-9-10-13-15-18-26-30-31-39-45-62-65-78-90-93-117-130-155-186-195-234-279-310-390-403-465-558-585-806-930-1,170-1,209-1,395-2,015-2,418-2,790-3,627-4,030-6,045-7,254-8,689-12,090-17,378-18,135-26,067-36,270-43,445-52,134-78,201-86,890-112,957-130,335-156,402-225,914-260,670-269,359-338,871-391,005-538,718-564,785-677,742-782,010-808,077-1,016,613-1,129,570-1,346,795-1,616,154-1,694,355-2,033,226-2,424,231-2,693,590-3,388,710-3,501,667-4,040,385-4,848,462-5,083,065-7,003,334-8,080,770-10,166,130-10,505,001-12,121,155-17,508,335-21,010,002-24,242,310-31,515,003-35,016,670-52,525,005-63,030,006-105,050,010-157,575,015-315,150,030

More Examples

Here are some more numbers to try:

315,150,028315,150,029315,150,031315,150,032
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