Q: What are the factor combinations of the number 7,358,735?

 A:
Positive:   1 x 73587355 x 147174723 x 31994561 x 120635115 x 63989305 x 241271049 x 70151403 x 5245
Negative: -1 x -7358735-5 x -1471747-23 x -319945-61 x -120635-115 x -63989-305 x -24127-1049 x -7015-1403 x -5245


How do I find the factor combinations of the number 7,358,735?

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 7,358,735, 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 7,358,735
-1 -7,358,735

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 7,358,735.

Example:
1 x 7,358,735 = 7,358,735
and
-1 x -7,358,735 = 7,358,735
Notice both answers equal 7,358,735

With that explanation out of the way, let's continue. Next, we take the number 7,358,735 and divide it by 2:

7,358,735 ÷ 2 = 3,679,367.5

If the quotient is a whole number, then 2 and 3,679,367.5 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 7,358,735
-1 -7,358,735

Now, we try dividing 7,358,735 by 3:

7,358,735 ÷ 3 = 2,452,911.6667

If the quotient is a whole number, then 3 and 2,452,911.6667 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 7,358,735
-1 -7,358,735

Let's try dividing by 4:

7,358,735 ÷ 4 = 1,839,683.75

If the quotient is a whole number, then 4 and 1,839,683.75 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 7,358,735
-1 7,358,735
Keep dividing by the next highest number until you cannot divide anymore.

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

1523611153051,0491,4035,2457,01524,12763,989120,635319,9451,471,7477,358,735
-1-5-23-61-115-305-1,049-1,403-5,245-7,015-24,127-63,989-120,635-319,945-1,471,747-7,358,735

More Examples

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