Q: What are the factor combinations of the number 42,321,409?

 A:
Positive:   1 x 4232140913 x 3255493
Negative: -1 x -42321409-13 x -3255493


How do I find the factor combinations of the number 42,321,409?

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 42,321,409, 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 42,321,409
-1 -42,321,409

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 42,321,409.

Example:
1 x 42,321,409 = 42,321,409
and
-1 x -42,321,409 = 42,321,409
Notice both answers equal 42,321,409

With that explanation out of the way, let's continue. Next, we take the number 42,321,409 and divide it by 2:

42,321,409 ÷ 2 = 21,160,704.5

If the quotient is a whole number, then 2 and 21,160,704.5 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 42,321,409
-1 -42,321,409

Now, we try dividing 42,321,409 by 3:

42,321,409 ÷ 3 = 14,107,136.3333

If the quotient is a whole number, then 3 and 14,107,136.3333 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 42,321,409
-1 -42,321,409

Let's try dividing by 4:

42,321,409 ÷ 4 = 10,580,352.25

If the quotient is a whole number, then 4 and 10,580,352.25 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 42,321,409
-1 42,321,409
Keep dividing by the next highest number until you cannot divide anymore.

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

1133,255,49342,321,409
-1-13-3,255,493-42,321,409

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 42,321,409:


Ask a Question