Q: What are the factor combinations of the number 138,242,419?

 A:
Positive:   1 x 1382424197 x 1974891717 x 8131907119 x 1161701163 x 8481131141 x 1211592771 x 498897127 x 19397
Negative: -1 x -138242419-7 x -19748917-17 x -8131907-119 x -1161701-163 x -848113-1141 x -121159-2771 x -49889-7127 x -19397


How do I find the factor combinations of the number 138,242,419?

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 138,242,419, 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.

1 138,242,419
-1 -138,242,419

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 138,242,419.

Example:
1 x 138,242,419 = 138,242,419
and
-1 x -138,242,419 = 138,242,419
Notice both answers equal 138,242,419

With that explanation out of the way, let's continue. Next, we take the number 138,242,419 and divide it by 2:

138,242,419 ÷ 2 = 69,121,209.5

If the quotient is a whole number, then 2 and 69,121,209.5 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:

1 138,242,419
-1 -138,242,419

Now, we try dividing 138,242,419 by 3:

138,242,419 ÷ 3 = 46,080,806.3333

If the quotient is a whole number, then 3 and 46,080,806.3333 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:

1 138,242,419
-1 -138,242,419

Let's try dividing by 4:

138,242,419 ÷ 4 = 34,560,604.75

If the quotient is a whole number, then 4 and 34,560,604.75 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:

1 138,242,419
-1 138,242,419
Keep dividing by the next highest number until you cannot divide anymore.

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

17171191631,1412,7717,12719,39749,889121,159848,1131,161,7018,131,90719,748,917138,242,419
-1-7-17-119-163-1,141-2,771-7,127-19,397-49,889-121,159-848,113-1,161,701-8,131,907-19,748,917-138,242,419

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