Q: What are the factor combinations of the number 23,251,529?

 A:
Positive:   1 x 232515297 x 332164717 x 136773749 x 474521103 x 225743119 x 195391271 x 85799721 x 32249833 x 279131751 x 132791897 x 122574607 x 5047
Negative: -1 x -23251529-7 x -3321647-17 x -1367737-49 x -474521-103 x -225743-119 x -195391-271 x -85799-721 x -32249-833 x -27913-1751 x -13279-1897 x -12257-4607 x -5047


How do I find the factor combinations of the number 23,251,529?

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 23,251,529, 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 23,251,529
-1 -23,251,529

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 23,251,529.

Example:
1 x 23,251,529 = 23,251,529
and
-1 x -23,251,529 = 23,251,529
Notice both answers equal 23,251,529

With that explanation out of the way, let's continue. Next, we take the number 23,251,529 and divide it by 2:

23,251,529 ÷ 2 = 11,625,764.5

If the quotient is a whole number, then 2 and 11,625,764.5 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 23,251,529
-1 -23,251,529

Now, we try dividing 23,251,529 by 3:

23,251,529 ÷ 3 = 7,750,509.6667

If the quotient is a whole number, then 3 and 7,750,509.6667 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 23,251,529
-1 -23,251,529

Let's try dividing by 4:

23,251,529 ÷ 4 = 5,812,882.25

If the quotient is a whole number, then 4 and 5,812,882.25 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 23,251,529
-1 23,251,529
Keep dividing by the next highest number until you cannot divide anymore.

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

1717491031192717218331,7511,8974,6075,04712,25713,27927,91332,24985,799195,391225,743474,5211,367,7373,321,64723,251,529
-1-7-17-49-103-119-271-721-833-1,751-1,897-4,607-5,047-12,257-13,279-27,913-32,249-85,799-195,391-225,743-474,521-1,367,737-3,321,647-23,251,529

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