Q: What are the factor combinations of the number 36,673,349?

 A:
Positive:   1 x 36673349
Negative: -1 x -36673349


How do I find the factor combinations of the number 36,673,349?

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 36,673,349, 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 36,673,349
-1 -36,673,349

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 36,673,349.

Example:
1 x 36,673,349 = 36,673,349
and
-1 x -36,673,349 = 36,673,349
Notice both answers equal 36,673,349

With that explanation out of the way, let's continue. Next, we take the number 36,673,349 and divide it by 2:

36,673,349 ÷ 2 = 18,336,674.5

If the quotient is a whole number, then 2 and 18,336,674.5 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 36,673,349
-1 -36,673,349

Now, we try dividing 36,673,349 by 3:

36,673,349 ÷ 3 = 12,224,449.6667

If the quotient is a whole number, then 3 and 12,224,449.6667 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 36,673,349
-1 -36,673,349

Let's try dividing by 4:

36,673,349 ÷ 4 = 9,168,337.25

If the quotient is a whole number, then 4 and 9,168,337.25 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 36,673,349
-1 36,673,349
Keep dividing by the next highest number until you cannot divide anymore.

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

136,673,349
-1-36,673,349

More Examples

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