Q: What are the factor combinations of the number 25,350,689?

 A:
Positive:   1 x 253506897 x 362152713 x 195005317 x 149121749 x 51736191 x 278579119 x 213031221 x 114709637 x 39797833 x 304331547 x 163872341 x 10829
Negative: -1 x -25350689-7 x -3621527-13 x -1950053-17 x -1491217-49 x -517361-91 x -278579-119 x -213031-221 x -114709-637 x -39797-833 x -30433-1547 x -16387-2341 x -10829


How do I find the factor combinations of the number 25,350,689?

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 25,350,689, 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 25,350,689
-1 -25,350,689

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 25,350,689.

Example:
1 x 25,350,689 = 25,350,689
and
-1 x -25,350,689 = 25,350,689
Notice both answers equal 25,350,689

With that explanation out of the way, let's continue. Next, we take the number 25,350,689 and divide it by 2:

25,350,689 ÷ 2 = 12,675,344.5

If the quotient is a whole number, then 2 and 12,675,344.5 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 25,350,689
-1 -25,350,689

Now, we try dividing 25,350,689 by 3:

25,350,689 ÷ 3 = 8,450,229.6667

If the quotient is a whole number, then 3 and 8,450,229.6667 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 25,350,689
-1 -25,350,689

Let's try dividing by 4:

25,350,689 ÷ 4 = 6,337,672.25

If the quotient is a whole number, then 4 and 6,337,672.25 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 25,350,689
-1 25,350,689
Keep dividing by the next highest number until you cannot divide anymore.

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

17131749911192216378331,5472,34110,82916,38730,43339,797114,709213,031278,579517,3611,491,2171,950,0533,621,52725,350,689
-1-7-13-17-49-91-119-221-637-833-1,547-2,341-10,829-16,387-30,433-39,797-114,709-213,031-278,579-517,361-1,491,217-1,950,053-3,621,527-25,350,689

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