Q: What are the factor combinations of the number 45,815?

 A:
Positive:   1 x 458155 x 91637 x 654511 x 416517 x 269535 x 130949 x 93555 x 83377 x 59585 x 539119 x 385187 x 245
Negative: -1 x -45815-5 x -9163-7 x -6545-11 x -4165-17 x -2695-35 x -1309-49 x -935-55 x -833-77 x -595-85 x -539-119 x -385-187 x -245


How do I find the factor combinations of the number 45,815?

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 45,815, 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 45,815
-1 -45,815

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 45,815.

Example:
1 x 45,815 = 45,815
and
-1 x -45,815 = 45,815
Notice both answers equal 45,815

With that explanation out of the way, let's continue. Next, we take the number 45,815 and divide it by 2:

45,815 ÷ 2 = 22,907.5

If the quotient is a whole number, then 2 and 22,907.5 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 45,815
-1 -45,815

Now, we try dividing 45,815 by 3:

45,815 ÷ 3 = 15,271.6667

If the quotient is a whole number, then 3 and 15,271.6667 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 45,815
-1 -45,815

Let's try dividing by 4:

45,815 ÷ 4 = 11,453.75

If the quotient is a whole number, then 4 and 11,453.75 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 45,815
-1 45,815
Keep dividing by the next highest number until you cannot divide anymore.

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

157111735495577851191872453855395958339351,3092,6954,1656,5459,16345,815
-1-5-7-11-17-35-49-55-77-85-119-187-245-385-539-595-833-935-1,309-2,695-4,165-6,545-9,163-45,815

More Examples

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