Q: What are the factor combinations of the number 42,114,127?

 A:
Positive:   1 x 4211412711 x 382855719 x 221653323 x 1831049209 x 201503253 x 166459437 x 963714807 x 8761
Negative: -1 x -42114127-11 x -3828557-19 x -2216533-23 x -1831049-209 x -201503-253 x -166459-437 x -96371-4807 x -8761


How do I find the factor combinations of the number 42,114,127?

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 42,114,127, 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 42,114,127
-1 -42,114,127

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 42,114,127.

Example:
1 x 42,114,127 = 42,114,127
and
-1 x -42,114,127 = 42,114,127
Notice both answers equal 42,114,127

With that explanation out of the way, let's continue. Next, we take the number 42,114,127 and divide it by 2:

42,114,127 ÷ 2 = 21,057,063.5

If the quotient is a whole number, then 2 and 21,057,063.5 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 42,114,127
-1 -42,114,127

Now, we try dividing 42,114,127 by 3:

42,114,127 ÷ 3 = 14,038,042.3333

If the quotient is a whole number, then 3 and 14,038,042.3333 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 42,114,127
-1 -42,114,127

Let's try dividing by 4:

42,114,127 ÷ 4 = 10,528,531.75

If the quotient is a whole number, then 4 and 10,528,531.75 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 42,114,127
-1 42,114,127
Keep dividing by the next highest number until you cannot divide anymore.

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

11119232092534374,8078,76196,371166,459201,5031,831,0492,216,5333,828,55742,114,127
-1-11-19-23-209-253-437-4,807-8,761-96,371-166,459-201,503-1,831,049-2,216,533-3,828,557-42,114,127

More Examples

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