Q: What are the factor combinations of the number 45,095?

 A:
Positive:   1 x 450955 x 901929 x 1555145 x 311
Negative: -1 x -45095-5 x -9019-29 x -1555-145 x -311


How do I find the factor combinations of the number 45,095?

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 45,095, 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 45,095
-1 -45,095

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 45,095.

Example:
1 x 45,095 = 45,095
and
-1 x -45,095 = 45,095
Notice both answers equal 45,095

With that explanation out of the way, let's continue. Next, we take the number 45,095 and divide it by 2:

45,095 ÷ 2 = 22,547.5

If the quotient is a whole number, then 2 and 22,547.5 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 45,095
-1 -45,095

Now, we try dividing 45,095 by 3:

45,095 ÷ 3 = 15,031.6667

If the quotient is a whole number, then 3 and 15,031.6667 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 45,095
-1 -45,095

Let's try dividing by 4:

45,095 ÷ 4 = 11,273.75

If the quotient is a whole number, then 4 and 11,273.75 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 45,095
-1 45,095
Keep dividing by the next highest number until you cannot divide anymore.

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

15291453111,5559,01945,095
-1-5-29-145-311-1,555-9,019-45,095

More Examples

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