Q: What are the factor combinations of the number 721,466,340?

 A:
Positive:   1 x 7214663402 x 3607331703 x 2404887804 x 1803665855 x 1442932686 x 1202443907 x 10306662010 x 7214663412 x 6012219514 x 5153331015 x 4809775620 x 3607331721 x 3435554028 x 2576665530 x 2404887835 x 2061332441 x 1759674042 x 1717777060 x 1202443970 x 1030666282 x 879837084 x 8588885105 x 6871108123 x 5865580140 x 5153331164 x 4399185205 x 3519348210 x 3435554246 x 2932790287 x 2513820410 x 1759674420 x 1717777492 x 1466395574 x 1256910615 x 1173116820 x 879837861 x 8379401148 x 6284551230 x 5865581435 x 5027641722 x 4189702460 x 2932792870 x 2513823444 x 2094854305 x 1675885740 x 1256918610 x 8379417220 x 41897
Negative: -1 x -721466340-2 x -360733170-3 x -240488780-4 x -180366585-5 x -144293268-6 x -120244390-7 x -103066620-10 x -72146634-12 x -60122195-14 x -51533310-15 x -48097756-20 x -36073317-21 x -34355540-28 x -25766655-30 x -24048878-35 x -20613324-41 x -17596740-42 x -17177770-60 x -12024439-70 x -10306662-82 x -8798370-84 x -8588885-105 x -6871108-123 x -5865580-140 x -5153331-164 x -4399185-205 x -3519348-210 x -3435554-246 x -2932790-287 x -2513820-410 x -1759674-420 x -1717777-492 x -1466395-574 x -1256910-615 x -1173116-820 x -879837-861 x -837940-1148 x -628455-1230 x -586558-1435 x -502764-1722 x -418970-2460 x -293279-2870 x -251382-3444 x -209485-4305 x -167588-5740 x -125691-8610 x -83794-17220 x -41897


How do I find the factor combinations of the number 721,466,340?

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 721,466,340, 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.

1 721,466,340
-1 -721,466,340

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 721,466,340.

Example:
1 x 721,466,340 = 721,466,340
and
-1 x -721,466,340 = 721,466,340
Notice both answers equal 721,466,340

With that explanation out of the way, let's continue. Next, we take the number 721,466,340 and divide it by 2:

721,466,340 ÷ 2 = 360,733,170

If the quotient is a whole number, then 2 and 360,733,170 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 2 360,733,170 721,466,340
-1 -2 -360,733,170 -721,466,340

Now, we try dividing 721,466,340 by 3:

721,466,340 ÷ 3 = 240,488,780

If the quotient is a whole number, then 3 and 240,488,780 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 3 240,488,780 360,733,170 721,466,340
-1 -2 -3 -240,488,780 -360,733,170 -721,466,340

Let's try dividing by 4:

721,466,340 ÷ 4 = 180,366,585

If the quotient is a whole number, then 4 and 180,366,585 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 4 180,366,585 240,488,780 360,733,170 721,466,340
-1 -2 -3 -4 -180,366,585 -240,488,780 -360,733,170 721,466,340
Keep dividing by the next highest number until you cannot divide anymore.

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

12345671012141520212830354142607082841051231401642052102462874104204925746158208611,1481,2301,4351,7222,4602,8703,4444,3055,7408,61017,22041,89783,794125,691167,588209,485251,382293,279418,970502,764586,558628,455837,940879,8371,173,1161,256,9101,466,3951,717,7771,759,6742,513,8202,932,7903,435,5543,519,3484,399,1855,153,3315,865,5806,871,1088,588,8858,798,37010,306,66212,024,43917,177,77017,596,74020,613,32424,048,87825,766,65534,355,54036,073,31748,097,75651,533,31060,122,19572,146,634103,066,620120,244,390144,293,268180,366,585240,488,780360,733,170721,466,340
-1-2-3-4-5-6-7-10-12-14-15-20-21-28-30-35-41-42-60-70-82-84-105-123-140-164-205-210-246-287-410-420-492-574-615-820-861-1,148-1,230-1,435-1,722-2,460-2,870-3,444-4,305-5,740-8,610-17,220-41,897-83,794-125,691-167,588-209,485-251,382-293,279-418,970-502,764-586,558-628,455-837,940-879,837-1,173,116-1,256,910-1,466,395-1,717,777-1,759,674-2,513,820-2,932,790-3,435,554-3,519,348-4,399,185-5,153,331-5,865,580-6,871,108-8,588,885-8,798,370-10,306,662-12,024,439-17,177,770-17,596,740-20,613,324-24,048,878-25,766,655-34,355,540-36,073,317-48,097,756-51,533,310-60,122,195-72,146,634-103,066,620-120,244,390-144,293,268-180,366,585-240,488,780-360,733,170-721,466,340

More Examples

Here are some more numbers to try:

721,466,338721,466,339721,466,341721,466,342
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