Q: What are the factor combinations of the number 7,478,723?

 A:
Positive:   1 x 74787237 x 106838919 x 39361729 x 25788749 x 152627133 x 56231203 x 36841277 x 26999551 x 13573931 x 80331421 x 52631939 x 3857
Negative: -1 x -7478723-7 x -1068389-19 x -393617-29 x -257887-49 x -152627-133 x -56231-203 x -36841-277 x -26999-551 x -13573-931 x -8033-1421 x -5263-1939 x -3857


How do I find the factor combinations of the number 7,478,723?

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 7,478,723, 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 7,478,723
-1 -7,478,723

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 7,478,723.

Example:
1 x 7,478,723 = 7,478,723
and
-1 x -7,478,723 = 7,478,723
Notice both answers equal 7,478,723

With that explanation out of the way, let's continue. Next, we take the number 7,478,723 and divide it by 2:

7,478,723 ÷ 2 = 3,739,361.5

If the quotient is a whole number, then 2 and 3,739,361.5 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 7,478,723
-1 -7,478,723

Now, we try dividing 7,478,723 by 3:

7,478,723 ÷ 3 = 2,492,907.6667

If the quotient is a whole number, then 3 and 2,492,907.6667 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 7,478,723
-1 -7,478,723

Let's try dividing by 4:

7,478,723 ÷ 4 = 1,869,680.75

If the quotient is a whole number, then 4 and 1,869,680.75 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 7,478,723
-1 7,478,723
Keep dividing by the next highest number until you cannot divide anymore.

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

171929491332032775519311,4211,9393,8575,2638,03313,57326,99936,84156,231152,627257,887393,6171,068,3897,478,723
-1-7-19-29-49-133-203-277-551-931-1,421-1,939-3,857-5,263-8,033-13,573-26,999-36,841-56,231-152,627-257,887-393,617-1,068,389-7,478,723

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