Q: What are the factor combinations of the number 23,165,345?

 A:
Positive:   1 x 231653455 x 46330697 x 330933529 x 79880535 x 661867145 x 159761203 x 114115787 x 29435841 x 275451015 x 228233935 x 58874205 x 5509
Negative: -1 x -23165345-5 x -4633069-7 x -3309335-29 x -798805-35 x -661867-145 x -159761-203 x -114115-787 x -29435-841 x -27545-1015 x -22823-3935 x -5887-4205 x -5509


How do I find the factor combinations of the number 23,165,345?

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 23,165,345, 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 23,165,345
-1 -23,165,345

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 23,165,345.

Example:
1 x 23,165,345 = 23,165,345
and
-1 x -23,165,345 = 23,165,345
Notice both answers equal 23,165,345

With that explanation out of the way, let's continue. Next, we take the number 23,165,345 and divide it by 2:

23,165,345 ÷ 2 = 11,582,672.5

If the quotient is a whole number, then 2 and 11,582,672.5 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 23,165,345
-1 -23,165,345

Now, we try dividing 23,165,345 by 3:

23,165,345 ÷ 3 = 7,721,781.6667

If the quotient is a whole number, then 3 and 7,721,781.6667 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 23,165,345
-1 -23,165,345

Let's try dividing by 4:

23,165,345 ÷ 4 = 5,791,336.25

If the quotient is a whole number, then 4 and 5,791,336.25 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 23,165,345
-1 23,165,345
Keep dividing by the next highest number until you cannot divide anymore.

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

15729351452037878411,0153,9354,2055,5095,88722,82327,54529,435114,115159,761661,867798,8053,309,3354,633,06923,165,345
-1-5-7-29-35-145-203-787-841-1,015-3,935-4,205-5,509-5,887-22,823-27,545-29,435-114,115-159,761-661,867-798,805-3,309,335-4,633,069-23,165,345

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