Q: What are the factor combinations of the number 42,541,213?

 A:
Positive:   1 x 4254121311 x 386738313 x 3272401143 x 297491521 x 81653571 x 745035731 x 74236281 x 6773
Negative: -1 x -42541213-11 x -3867383-13 x -3272401-143 x -297491-521 x -81653-571 x -74503-5731 x -7423-6281 x -6773


How do I find the factor combinations of the number 42,541,213?

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 42,541,213, 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 42,541,213
-1 -42,541,213

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 42,541,213.

Example:
1 x 42,541,213 = 42,541,213
and
-1 x -42,541,213 = 42,541,213
Notice both answers equal 42,541,213

With that explanation out of the way, let's continue. Next, we take the number 42,541,213 and divide it by 2:

42,541,213 ÷ 2 = 21,270,606.5

If the quotient is a whole number, then 2 and 21,270,606.5 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 42,541,213
-1 -42,541,213

Now, we try dividing 42,541,213 by 3:

42,541,213 ÷ 3 = 14,180,404.3333

If the quotient is a whole number, then 3 and 14,180,404.3333 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 42,541,213
-1 -42,541,213

Let's try dividing by 4:

42,541,213 ÷ 4 = 10,635,303.25

If the quotient is a whole number, then 4 and 10,635,303.25 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 42,541,213
-1 42,541,213
Keep dividing by the next highest number until you cannot divide anymore.

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

111131435215715,7316,2816,7737,42374,50381,653297,4913,272,4013,867,38342,541,213
-1-11-13-143-521-571-5,731-6,281-6,773-7,423-74,503-81,653-297,491-3,272,401-3,867,383-42,541,213

More Examples

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