Q: What are the factor combinations of the number 15,122,525?

 A:
Positive:   1 x 151225255 x 302450511 x 137477525 x 60490155 x 274955127 x 119075275 x 54991433 x 34925635 x 238151397 x 108252165 x 69853175 x 4763
Negative: -1 x -15122525-5 x -3024505-11 x -1374775-25 x -604901-55 x -274955-127 x -119075-275 x -54991-433 x -34925-635 x -23815-1397 x -10825-2165 x -6985-3175 x -4763


How do I find the factor combinations of the number 15,122,525?

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 15,122,525, 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 15,122,525
-1 -15,122,525

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 15,122,525.

Example:
1 x 15,122,525 = 15,122,525
and
-1 x -15,122,525 = 15,122,525
Notice both answers equal 15,122,525

With that explanation out of the way, let's continue. Next, we take the number 15,122,525 and divide it by 2:

15,122,525 ÷ 2 = 7,561,262.5

If the quotient is a whole number, then 2 and 7,561,262.5 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 15,122,525
-1 -15,122,525

Now, we try dividing 15,122,525 by 3:

15,122,525 ÷ 3 = 5,040,841.6667

If the quotient is a whole number, then 3 and 5,040,841.6667 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 15,122,525
-1 -15,122,525

Let's try dividing by 4:

15,122,525 ÷ 4 = 3,780,631.25

If the quotient is a whole number, then 4 and 3,780,631.25 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 15,122,525
-1 15,122,525
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551272754336351,3972,1653,1754,7636,98510,82523,81534,92554,991119,075274,955604,9011,374,7753,024,50515,122,525
-1-5-11-25-55-127-275-433-635-1,397-2,165-3,175-4,763-6,985-10,825-23,815-34,925-54,991-119,075-274,955-604,901-1,374,775-3,024,505-15,122,525

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