Q: What are the factor combinations of the number 42,536,431?

 A:
Positive:   1 x 425364317 x 607663317 x 2502143119 x 357449271 x 1569611319 x 322491897 x 224234607 x 9233
Negative: -1 x -42536431-7 x -6076633-17 x -2502143-119 x -357449-271 x -156961-1319 x -32249-1897 x -22423-4607 x -9233


How do I find the factor combinations of the number 42,536,431?

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 42,536,431, 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 42,536,431
-1 -42,536,431

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 42,536,431.

Example:
1 x 42,536,431 = 42,536,431
and
-1 x -42,536,431 = 42,536,431
Notice both answers equal 42,536,431

With that explanation out of the way, let's continue. Next, we take the number 42,536,431 and divide it by 2:

42,536,431 ÷ 2 = 21,268,215.5

If the quotient is a whole number, then 2 and 21,268,215.5 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 42,536,431
-1 -42,536,431

Now, we try dividing 42,536,431 by 3:

42,536,431 ÷ 3 = 14,178,810.3333

If the quotient is a whole number, then 3 and 14,178,810.3333 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 42,536,431
-1 -42,536,431

Let's try dividing by 4:

42,536,431 ÷ 4 = 10,634,107.75

If the quotient is a whole number, then 4 and 10,634,107.75 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 42,536,431
-1 42,536,431
Keep dividing by the next highest number until you cannot divide anymore.

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

17171192711,3191,8974,6079,23322,42332,249156,961357,4492,502,1436,076,63342,536,431
-1-7-17-119-271-1,319-1,897-4,607-9,233-22,423-32,249-156,961-357,449-2,502,143-6,076,633-42,536,431

More Examples

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