Q: What are the factor combinations of the number 42,024,109?

 A:
Positive:   1 x 4202410989 x 472181149 x 2820413169 x 13261
Negative: -1 x -42024109-89 x -472181-149 x -282041-3169 x -13261


How do I find the factor combinations of the number 42,024,109?

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 42,024,109, 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 42,024,109
-1 -42,024,109

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 42,024,109.

Example:
1 x 42,024,109 = 42,024,109
and
-1 x -42,024,109 = 42,024,109
Notice both answers equal 42,024,109

With that explanation out of the way, let's continue. Next, we take the number 42,024,109 and divide it by 2:

42,024,109 ÷ 2 = 21,012,054.5

If the quotient is a whole number, then 2 and 21,012,054.5 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 42,024,109
-1 -42,024,109

Now, we try dividing 42,024,109 by 3:

42,024,109 ÷ 3 = 14,008,036.3333

If the quotient is a whole number, then 3 and 14,008,036.3333 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 42,024,109
-1 -42,024,109

Let's try dividing by 4:

42,024,109 ÷ 4 = 10,506,027.25

If the quotient is a whole number, then 4 and 10,506,027.25 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 42,024,109
-1 42,024,109
Keep dividing by the next highest number until you cannot divide anymore.

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

1891493,16913,261282,041472,18142,024,109
-1-89-149-3,169-13,261-282,041-472,181-42,024,109

More Examples

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