Q: What are the factor combinations of the number 7,401,515?

 A:
Positive:   1 x 74015155 x 148030311 x 67286523 x 32180555 x 134573115 x 64361253 x 292551265 x 5851
Negative: -1 x -7401515-5 x -1480303-11 x -672865-23 x -321805-55 x -134573-115 x -64361-253 x -29255-1265 x -5851


How do I find the factor combinations of the number 7,401,515?

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 7,401,515, 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 7,401,515
-1 -7,401,515

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 7,401,515.

Example:
1 x 7,401,515 = 7,401,515
and
-1 x -7,401,515 = 7,401,515
Notice both answers equal 7,401,515

With that explanation out of the way, let's continue. Next, we take the number 7,401,515 and divide it by 2:

7,401,515 ÷ 2 = 3,700,757.5

If the quotient is a whole number, then 2 and 3,700,757.5 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 7,401,515
-1 -7,401,515

Now, we try dividing 7,401,515 by 3:

7,401,515 ÷ 3 = 2,467,171.6667

If the quotient is a whole number, then 3 and 2,467,171.6667 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 7,401,515
-1 -7,401,515

Let's try dividing by 4:

7,401,515 ÷ 4 = 1,850,378.75

If the quotient is a whole number, then 4 and 1,850,378.75 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 7,401,515
-1 7,401,515
Keep dividing by the next highest number until you cannot divide anymore.

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

151123551152531,2655,85129,25564,361134,573321,805672,8651,480,3037,401,515
-1-5-11-23-55-115-253-1,265-5,851-29,255-64,361-134,573-321,805-672,865-1,480,303-7,401,515

More Examples

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