Q: What are the factor combinations of the number 42,134,323?

 A:
Positive:   1 x 421343237 x 601918911 x 383039377 x 547199173 x 2435511211 x 347931903 x 221413163 x 13321
Negative: -1 x -42134323-7 x -6019189-11 x -3830393-77 x -547199-173 x -243551-1211 x -34793-1903 x -22141-3163 x -13321


How do I find the factor combinations of the number 42,134,323?

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 42,134,323, 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 42,134,323
-1 -42,134,323

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 42,134,323.

Example:
1 x 42,134,323 = 42,134,323
and
-1 x -42,134,323 = 42,134,323
Notice both answers equal 42,134,323

With that explanation out of the way, let's continue. Next, we take the number 42,134,323 and divide it by 2:

42,134,323 ÷ 2 = 21,067,161.5

If the quotient is a whole number, then 2 and 21,067,161.5 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 42,134,323
-1 -42,134,323

Now, we try dividing 42,134,323 by 3:

42,134,323 ÷ 3 = 14,044,774.3333

If the quotient is a whole number, then 3 and 14,044,774.3333 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 42,134,323
-1 -42,134,323

Let's try dividing by 4:

42,134,323 ÷ 4 = 10,533,580.75

If the quotient is a whole number, then 4 and 10,533,580.75 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 42,134,323
-1 42,134,323
Keep dividing by the next highest number until you cannot divide anymore.

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

1711771731,2111,9033,16313,32122,14134,793243,551547,1993,830,3936,019,18942,134,323
-1-7-11-77-173-1,211-1,903-3,163-13,321-22,141-34,793-243,551-547,199-3,830,393-6,019,189-42,134,323

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