Q: What are the factor combinations of the number 731,026,501?

 A:
Positive:   1 x 73102650119 x 3847507937 x 1975747361 x 11984041703 x 10398671159 x 6307392257 x 32389317047 x 42883
Negative: -1 x -731026501-19 x -38475079-37 x -19757473-61 x -11984041-703 x -1039867-1159 x -630739-2257 x -323893-17047 x -42883


How do I find the factor combinations of the number 731,026,501?

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 731,026,501, 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.

1 731,026,501
-1 -731,026,501

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 731,026,501.

Example:
1 x 731,026,501 = 731,026,501
and
-1 x -731,026,501 = 731,026,501
Notice both answers equal 731,026,501

With that explanation out of the way, let's continue. Next, we take the number 731,026,501 and divide it by 2:

731,026,501 ÷ 2 = 365,513,250.5

If the quotient is a whole number, then 2 and 365,513,250.5 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:

1 731,026,501
-1 -731,026,501

Now, we try dividing 731,026,501 by 3:

731,026,501 ÷ 3 = 243,675,500.3333

If the quotient is a whole number, then 3 and 243,675,500.3333 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:

1 731,026,501
-1 -731,026,501

Let's try dividing by 4:

731,026,501 ÷ 4 = 182,756,625.25

If the quotient is a whole number, then 4 and 182,756,625.25 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:

1 731,026,501
-1 731,026,501
Keep dividing by the next highest number until you cannot divide anymore.

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

11937617031,1592,25717,04742,883323,893630,7391,039,86711,984,04119,757,47338,475,079731,026,501
-1-19-37-61-703-1,159-2,257-17,047-42,883-323,893-630,739-1,039,867-11,984,041-19,757,473-38,475,079-731,026,501

More Examples

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