Q: What are the factor combinations of the number 1,502,345?

 A:
Positive:   1 x 15023455 x 30046913 x 11556529 x 5180565 x 23113145 x 10361377 x 3985797 x 1885
Negative: -1 x -1502345-5 x -300469-13 x -115565-29 x -51805-65 x -23113-145 x -10361-377 x -3985-797 x -1885


How do I find the factor combinations of the number 1,502,345?

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 1,502,345, 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 1,502,345
-1 -1,502,345

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 1,502,345.

Example:
1 x 1,502,345 = 1,502,345
and
-1 x -1,502,345 = 1,502,345
Notice both answers equal 1,502,345

With that explanation out of the way, let's continue. Next, we take the number 1,502,345 and divide it by 2:

1,502,345 ÷ 2 = 751,172.5

If the quotient is a whole number, then 2 and 751,172.5 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 1,502,345
-1 -1,502,345

Now, we try dividing 1,502,345 by 3:

1,502,345 ÷ 3 = 500,781.6667

If the quotient is a whole number, then 3 and 500,781.6667 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 1,502,345
-1 -1,502,345

Let's try dividing by 4:

1,502,345 ÷ 4 = 375,586.25

If the quotient is a whole number, then 4 and 375,586.25 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 1,502,345
-1 1,502,345
Keep dividing by the next highest number until you cannot divide anymore.

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

151329651453777971,8853,98510,36123,11351,805115,565300,4691,502,345
-1-5-13-29-65-145-377-797-1,885-3,985-10,361-23,113-51,805-115,565-300,469-1,502,345

More Examples

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