Q: What are the factor combinations of the number 7,138,415?

 A:
Positive:   1 x 71384155 x 142768383 x 86005103 x 69305167 x 42745415 x 17201515 x 13861835 x 8549
Negative: -1 x -7138415-5 x -1427683-83 x -86005-103 x -69305-167 x -42745-415 x -17201-515 x -13861-835 x -8549


How do I find the factor combinations of the number 7,138,415?

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 7,138,415, 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 7,138,415
-1 -7,138,415

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 7,138,415.

Example:
1 x 7,138,415 = 7,138,415
and
-1 x -7,138,415 = 7,138,415
Notice both answers equal 7,138,415

With that explanation out of the way, let's continue. Next, we take the number 7,138,415 and divide it by 2:

7,138,415 ÷ 2 = 3,569,207.5

If the quotient is a whole number, then 2 and 3,569,207.5 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 7,138,415
-1 -7,138,415

Now, we try dividing 7,138,415 by 3:

7,138,415 ÷ 3 = 2,379,471.6667

If the quotient is a whole number, then 3 and 2,379,471.6667 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 7,138,415
-1 -7,138,415

Let's try dividing by 4:

7,138,415 ÷ 4 = 1,784,603.75

If the quotient is a whole number, then 4 and 1,784,603.75 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 7,138,415
-1 7,138,415
Keep dividing by the next highest number until you cannot divide anymore.

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

15831031674155158358,54913,86117,20142,74569,30586,0051,427,6837,138,415
-1-5-83-103-167-415-515-835-8,549-13,861-17,201-42,745-69,305-86,005-1,427,683-7,138,415

More Examples

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