Q: What are the factor combinations of the number 23,969,225?

 A:
Positive:   1 x 239692255 x 47938457 x 342417525 x 95876929 x 82652535 x 684835145 x 165305175 x 136967203 x 118075725 x 330611015 x 236154723 x 5075
Negative: -1 x -23969225-5 x -4793845-7 x -3424175-25 x -958769-29 x -826525-35 x -684835-145 x -165305-175 x -136967-203 x -118075-725 x -33061-1015 x -23615-4723 x -5075


How do I find the factor combinations of the number 23,969,225?

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 23,969,225, 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 23,969,225
-1 -23,969,225

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 23,969,225.

Example:
1 x 23,969,225 = 23,969,225
and
-1 x -23,969,225 = 23,969,225
Notice both answers equal 23,969,225

With that explanation out of the way, let's continue. Next, we take the number 23,969,225 and divide it by 2:

23,969,225 ÷ 2 = 11,984,612.5

If the quotient is a whole number, then 2 and 11,984,612.5 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 23,969,225
-1 -23,969,225

Now, we try dividing 23,969,225 by 3:

23,969,225 ÷ 3 = 7,989,741.6667

If the quotient is a whole number, then 3 and 7,989,741.6667 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 23,969,225
-1 -23,969,225

Let's try dividing by 4:

23,969,225 ÷ 4 = 5,992,306.25

If the quotient is a whole number, then 4 and 5,992,306.25 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 23,969,225
-1 23,969,225
Keep dividing by the next highest number until you cannot divide anymore.

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

1572529351451752037251,0154,7235,07523,61533,061118,075136,967165,305684,835826,525958,7693,424,1754,793,84523,969,225
-1-5-7-25-29-35-145-175-203-725-1,015-4,723-5,075-23,615-33,061-118,075-136,967-165,305-684,835-826,525-958,769-3,424,175-4,793,845-23,969,225

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