Q: What are the factor combinations of the number 415,300,325?

 A:
Positive:   1 x 4153003255 x 8306006511 x 3775457525 x 1661201355 x 7550915157 x 2645225275 x 1510183785 x 5290451727 x 2404753925 x 1058098635 x 480959619 x 43175
Negative: -1 x -415300325-5 x -83060065-11 x -37754575-25 x -16612013-55 x -7550915-157 x -2645225-275 x -1510183-785 x -529045-1727 x -240475-3925 x -105809-8635 x -48095-9619 x -43175


How do I find the factor combinations of the number 415,300,325?

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 415,300,325, 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.

1 415,300,325
-1 -415,300,325

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 415,300,325.

Example:
1 x 415,300,325 = 415,300,325
and
-1 x -415,300,325 = 415,300,325
Notice both answers equal 415,300,325

With that explanation out of the way, let's continue. Next, we take the number 415,300,325 and divide it by 2:

415,300,325 ÷ 2 = 207,650,162.5

If the quotient is a whole number, then 2 and 207,650,162.5 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:

1 415,300,325
-1 -415,300,325

Now, we try dividing 415,300,325 by 3:

415,300,325 ÷ 3 = 138,433,441.6667

If the quotient is a whole number, then 3 and 138,433,441.6667 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:

1 415,300,325
-1 -415,300,325

Let's try dividing by 4:

415,300,325 ÷ 4 = 103,825,081.25

If the quotient is a whole number, then 4 and 103,825,081.25 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:

1 415,300,325
-1 415,300,325
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551572757851,7273,9258,6359,61943,17548,095105,809240,475529,0451,510,1832,645,2257,550,91516,612,01337,754,57583,060,065415,300,325
-1-5-11-25-55-157-275-785-1,727-3,925-8,635-9,619-43,175-48,095-105,809-240,475-529,045-1,510,183-2,645,225-7,550,915-16,612,013-37,754,575-83,060,065-415,300,325

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