Q: What are the factor combinations of the number 232,102,745?

 A:
Positive:   1 x 2321027455 x 464205497 x 3315753535 x 6631507307 x 7560351535 x 1512072149 x 10800510745 x 21601
Negative: -1 x -232102745-5 x -46420549-7 x -33157535-35 x -6631507-307 x -756035-1535 x -151207-2149 x -108005-10745 x -21601


How do I find the factor combinations of the number 232,102,745?

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 232,102,745, 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.

1 232,102,745
-1 -232,102,745

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 232,102,745.

Example:
1 x 232,102,745 = 232,102,745
and
-1 x -232,102,745 = 232,102,745
Notice both answers equal 232,102,745

With that explanation out of the way, let's continue. Next, we take the number 232,102,745 and divide it by 2:

232,102,745 ÷ 2 = 116,051,372.5

If the quotient is a whole number, then 2 and 116,051,372.5 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:

1 232,102,745
-1 -232,102,745

Now, we try dividing 232,102,745 by 3:

232,102,745 ÷ 3 = 77,367,581.6667

If the quotient is a whole number, then 3 and 77,367,581.6667 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:

1 232,102,745
-1 -232,102,745

Let's try dividing by 4:

232,102,745 ÷ 4 = 58,025,686.25

If the quotient is a whole number, then 4 and 58,025,686.25 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:

1 232,102,745
-1 232,102,745
Keep dividing by the next highest number until you cannot divide anymore.

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

157353071,5352,14910,74521,601108,005151,207756,0356,631,50733,157,53546,420,549232,102,745
-1-5-7-35-307-1,535-2,149-10,745-21,601-108,005-151,207-756,035-6,631,507-33,157,535-46,420,549-232,102,745

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