Q: What are the factor combinations of the number 7,300,123?

 A:
Positive:   1 x 730012317 x 42941919 x 38421797 x 75259233 x 31331323 x 226011649 x 44271843 x 3961
Negative: -1 x -7300123-17 x -429419-19 x -384217-97 x -75259-233 x -31331-323 x -22601-1649 x -4427-1843 x -3961


How do I find the factor combinations of the number 7,300,123?

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 7,300,123, 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 7,300,123
-1 -7,300,123

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 7,300,123.

Example:
1 x 7,300,123 = 7,300,123
and
-1 x -7,300,123 = 7,300,123
Notice both answers equal 7,300,123

With that explanation out of the way, let's continue. Next, we take the number 7,300,123 and divide it by 2:

7,300,123 ÷ 2 = 3,650,061.5

If the quotient is a whole number, then 2 and 3,650,061.5 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 7,300,123
-1 -7,300,123

Now, we try dividing 7,300,123 by 3:

7,300,123 ÷ 3 = 2,433,374.3333

If the quotient is a whole number, then 3 and 2,433,374.3333 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 7,300,123
-1 -7,300,123

Let's try dividing by 4:

7,300,123 ÷ 4 = 1,825,030.75

If the quotient is a whole number, then 4 and 1,825,030.75 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 7,300,123
-1 7,300,123
Keep dividing by the next highest number until you cannot divide anymore.

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

11719972333231,6491,8433,9614,42722,60131,33175,259384,217429,4197,300,123
-1-17-19-97-233-323-1,649-1,843-3,961-4,427-22,601-31,331-75,259-384,217-429,419-7,300,123

More Examples

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