Q: What are the factor combinations of the number 27,038,725?

 A:
Positive:   1 x 270387255 x 54077457 x 386267525 x 108154935 x 772535175 x 154507367 x 73675421 x 642251835 x 147352105 x 128452569 x 105252947 x 9175
Negative: -1 x -27038725-5 x -5407745-7 x -3862675-25 x -1081549-35 x -772535-175 x -154507-367 x -73675-421 x -64225-1835 x -14735-2105 x -12845-2569 x -10525-2947 x -9175


How do I find the factor combinations of the number 27,038,725?

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 27,038,725, 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 27,038,725
-1 -27,038,725

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 27,038,725.

Example:
1 x 27,038,725 = 27,038,725
and
-1 x -27,038,725 = 27,038,725
Notice both answers equal 27,038,725

With that explanation out of the way, let's continue. Next, we take the number 27,038,725 and divide it by 2:

27,038,725 ÷ 2 = 13,519,362.5

If the quotient is a whole number, then 2 and 13,519,362.5 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 27,038,725
-1 -27,038,725

Now, we try dividing 27,038,725 by 3:

27,038,725 ÷ 3 = 9,012,908.3333

If the quotient is a whole number, then 3 and 9,012,908.3333 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 27,038,725
-1 -27,038,725

Let's try dividing by 4:

27,038,725 ÷ 4 = 6,759,681.25

If the quotient is a whole number, then 4 and 6,759,681.25 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 27,038,725
-1 27,038,725
Keep dividing by the next highest number until you cannot divide anymore.

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

15725351753674211,8352,1052,5692,9479,17510,52512,84514,73564,22573,675154,507772,5351,081,5493,862,6755,407,74527,038,725
-1-5-7-25-35-175-367-421-1,835-2,105-2,569-2,947-9,175-10,525-12,845-14,735-64,225-73,675-154,507-772,535-1,081,549-3,862,675-5,407,745-27,038,725

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