Q: What are the factor combinations of the number 23,144,765?

 A:
Positive:   1 x 231447655 x 46289537 x 330639535 x 661279457 x 506451447 x 159952285 x 101293199 x 7235
Negative: -1 x -23144765-5 x -4628953-7 x -3306395-35 x -661279-457 x -50645-1447 x -15995-2285 x -10129-3199 x -7235


How do I find the factor combinations of the number 23,144,765?

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 23,144,765, 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 23,144,765
-1 -23,144,765

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 23,144,765.

Example:
1 x 23,144,765 = 23,144,765
and
-1 x -23,144,765 = 23,144,765
Notice both answers equal 23,144,765

With that explanation out of the way, let's continue. Next, we take the number 23,144,765 and divide it by 2:

23,144,765 ÷ 2 = 11,572,382.5

If the quotient is a whole number, then 2 and 11,572,382.5 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 23,144,765
-1 -23,144,765

Now, we try dividing 23,144,765 by 3:

23,144,765 ÷ 3 = 7,714,921.6667

If the quotient is a whole number, then 3 and 7,714,921.6667 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 23,144,765
-1 -23,144,765

Let's try dividing by 4:

23,144,765 ÷ 4 = 5,786,191.25

If the quotient is a whole number, then 4 and 5,786,191.25 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 23,144,765
-1 23,144,765
Keep dividing by the next highest number until you cannot divide anymore.

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

157354571,4472,2853,1997,23510,12915,99550,645661,2793,306,3954,628,95323,144,765
-1-5-7-35-457-1,447-2,285-3,199-7,235-10,129-15,995-50,645-661,279-3,306,395-4,628,953-23,144,765

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