Q: What are the factor combinations of the number 36,513,025?

 A:
Positive:   1 x 365130255 x 730260517 x 214782525 x 146052153 x 68892585 x 429565265 x 137785425 x 85913901 x 405251325 x 275571621 x 225254505 x 8105
Negative: -1 x -36513025-5 x -7302605-17 x -2147825-25 x -1460521-53 x -688925-85 x -429565-265 x -137785-425 x -85913-901 x -40525-1325 x -27557-1621 x -22525-4505 x -8105


How do I find the factor combinations of the number 36,513,025?

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 36,513,025, 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 36,513,025
-1 -36,513,025

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 36,513,025.

Example:
1 x 36,513,025 = 36,513,025
and
-1 x -36,513,025 = 36,513,025
Notice both answers equal 36,513,025

With that explanation out of the way, let's continue. Next, we take the number 36,513,025 and divide it by 2:

36,513,025 ÷ 2 = 18,256,512.5

If the quotient is a whole number, then 2 and 18,256,512.5 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 36,513,025
-1 -36,513,025

Now, we try dividing 36,513,025 by 3:

36,513,025 ÷ 3 = 12,171,008.3333

If the quotient is a whole number, then 3 and 12,171,008.3333 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 36,513,025
-1 -36,513,025

Let's try dividing by 4:

36,513,025 ÷ 4 = 9,128,256.25

If the quotient is a whole number, then 4 and 9,128,256.25 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 36,513,025
-1 36,513,025
Keep dividing by the next highest number until you cannot divide anymore.

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

15172553852654259011,3251,6214,5058,10522,52527,55740,52585,913137,785429,565688,9251,460,5212,147,8257,302,60536,513,025
-1-5-17-25-53-85-265-425-901-1,325-1,621-4,505-8,105-22,525-27,557-40,525-85,913-137,785-429,565-688,925-1,460,521-2,147,825-7,302,605-36,513,025

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