Q: What are the factor combinations of the number 42,104,207?

 A:
Positive:   1 x 4210420753 x 79441967 x 62842171 x 593017167 x 2521213551 x 118573763 x 111894757 x 8851
Negative: -1 x -42104207-53 x -794419-67 x -628421-71 x -593017-167 x -252121-3551 x -11857-3763 x -11189-4757 x -8851


How do I find the factor combinations of the number 42,104,207?

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 42,104,207, 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 42,104,207
-1 -42,104,207

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 42,104,207.

Example:
1 x 42,104,207 = 42,104,207
and
-1 x -42,104,207 = 42,104,207
Notice both answers equal 42,104,207

With that explanation out of the way, let's continue. Next, we take the number 42,104,207 and divide it by 2:

42,104,207 ÷ 2 = 21,052,103.5

If the quotient is a whole number, then 2 and 21,052,103.5 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 42,104,207
-1 -42,104,207

Now, we try dividing 42,104,207 by 3:

42,104,207 ÷ 3 = 14,034,735.6667

If the quotient is a whole number, then 3 and 14,034,735.6667 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 42,104,207
-1 -42,104,207

Let's try dividing by 4:

42,104,207 ÷ 4 = 10,526,051.75

If the quotient is a whole number, then 4 and 10,526,051.75 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 42,104,207
-1 42,104,207
Keep dividing by the next highest number until you cannot divide anymore.

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

15367711673,5513,7634,7578,85111,18911,857252,121593,017628,421794,41942,104,207
-1-53-67-71-167-3,551-3,763-4,757-8,851-11,189-11,857-252,121-593,017-628,421-794,419-42,104,207

More Examples

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