Q: What are the factor combinations of the number 407,286,080?

 A:
Positive:   1 x 4072860802 x 2036430404 x 1018215205 x 814572168 x 5091076010 x 4072860816 x 2545538020 x 2036430432 x 1272769040 x 1018215264 x 636384579 x 515552080 x 5091076158 x 2577760160 x 2545538316 x 1288880320 x 1272769395 x 1031104632 x 644440790 x 5155521264 x 3222201580 x 2577762528 x 1611103160 x 1288885056 x 805556320 x 6444412640 x 3222216111 x 25280
Negative: -1 x -407286080-2 x -203643040-4 x -101821520-5 x -81457216-8 x -50910760-10 x -40728608-16 x -25455380-20 x -20364304-32 x -12727690-40 x -10182152-64 x -6363845-79 x -5155520-80 x -5091076-158 x -2577760-160 x -2545538-316 x -1288880-320 x -1272769-395 x -1031104-632 x -644440-790 x -515552-1264 x -322220-1580 x -257776-2528 x -161110-3160 x -128888-5056 x -80555-6320 x -64444-12640 x -32222-16111 x -25280


How do I find the factor combinations of the number 407,286,080?

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 407,286,080, 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.

1 407,286,080
-1 -407,286,080

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 407,286,080.

Example:
1 x 407,286,080 = 407,286,080
and
-1 x -407,286,080 = 407,286,080
Notice both answers equal 407,286,080

With that explanation out of the way, let's continue. Next, we take the number 407,286,080 and divide it by 2:

407,286,080 ÷ 2 = 203,643,040

If the quotient is a whole number, then 2 and 203,643,040 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 2 203,643,040 407,286,080
-1 -2 -203,643,040 -407,286,080

Now, we try dividing 407,286,080 by 3:

407,286,080 ÷ 3 = 135,762,026.6667

If the quotient is a whole number, then 3 and 135,762,026.6667 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 2 203,643,040 407,286,080
-1 -2 -203,643,040 -407,286,080

Let's try dividing by 4:

407,286,080 ÷ 4 = 101,821,520

If the quotient is a whole number, then 4 and 101,821,520 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 4 101,821,520 203,643,040 407,286,080
-1 -2 -4 -101,821,520 -203,643,040 407,286,080
Keep dividing by the next highest number until you cannot divide anymore.

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

1245810162032406479801581603163203956327901,2641,5802,5283,1605,0566,32012,64016,11125,28032,22264,44480,555128,888161,110257,776322,220515,552644,4401,031,1041,272,7691,288,8802,545,5382,577,7605,091,0765,155,5206,363,84510,182,15212,727,69020,364,30425,455,38040,728,60850,910,76081,457,216101,821,520203,643,040407,286,080
-1-2-4-5-8-10-16-20-32-40-64-79-80-158-160-316-320-395-632-790-1,264-1,580-2,528-3,160-5,056-6,320-12,640-16,111-25,280-32,222-64,444-80,555-128,888-161,110-257,776-322,220-515,552-644,440-1,031,104-1,272,769-1,288,880-2,545,538-2,577,760-5,091,076-5,155,520-6,363,845-10,182,152-12,727,690-20,364,304-25,455,380-40,728,608-50,910,760-81,457,216-101,821,520-203,643,040-407,286,080

More Examples

Here are some more numbers to try:

407,286,078407,286,079407,286,081407,286,082
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