Q: What are the factor combinations of the number 1,500,415?

 A:
Positive:   1 x 15004155 x 3000837 x 21434535 x 42869163 x 9205263 x 5705815 x 18411141 x 1315
Negative: -1 x -1500415-5 x -300083-7 x -214345-35 x -42869-163 x -9205-263 x -5705-815 x -1841-1141 x -1315


How do I find the factor combinations of the number 1,500,415?

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 1,500,415, 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 1,500,415
-1 -1,500,415

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 1,500,415.

Example:
1 x 1,500,415 = 1,500,415
and
-1 x -1,500,415 = 1,500,415
Notice both answers equal 1,500,415

With that explanation out of the way, let's continue. Next, we take the number 1,500,415 and divide it by 2:

1,500,415 ÷ 2 = 750,207.5

If the quotient is a whole number, then 2 and 750,207.5 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 1,500,415
-1 -1,500,415

Now, we try dividing 1,500,415 by 3:

1,500,415 ÷ 3 = 500,138.3333

If the quotient is a whole number, then 3 and 500,138.3333 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 1,500,415
-1 -1,500,415

Let's try dividing by 4:

1,500,415 ÷ 4 = 375,103.75

If the quotient is a whole number, then 4 and 375,103.75 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 1,500,415
-1 1,500,415
Keep dividing by the next highest number until you cannot divide anymore.

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

157351632638151,1411,3151,8415,7059,20542,869214,345300,0831,500,415
-1-5-7-35-163-263-815-1,141-1,315-1,841-5,705-9,205-42,869-214,345-300,083-1,500,415

More Examples

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