Q: What are the factor combinations of the number 382,025?

 A:
Positive:   1 x 3820255 x 764057 x 5457525 x 1528135 x 1091537 x 1032559 x 6475175 x 2183185 x 2065259 x 1475295 x 1295413 x 925
Negative: -1 x -382025-5 x -76405-7 x -54575-25 x -15281-35 x -10915-37 x -10325-59 x -6475-175 x -2183-185 x -2065-259 x -1475-295 x -1295-413 x -925


How do I find the factor combinations of the number 382,025?

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 382,025, 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.

1 382,025
-1 -382,025

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 382,025.

Example:
1 x 382,025 = 382,025
and
-1 x -382,025 = 382,025
Notice both answers equal 382,025

With that explanation out of the way, let's continue. Next, we take the number 382,025 and divide it by 2:

382,025 ÷ 2 = 191,012.5

If the quotient is a whole number, then 2 and 191,012.5 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:

1 382,025
-1 -382,025

Now, we try dividing 382,025 by 3:

382,025 ÷ 3 = 127,341.6667

If the quotient is a whole number, then 3 and 127,341.6667 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:

1 382,025
-1 -382,025

Let's try dividing by 4:

382,025 ÷ 4 = 95,506.25

If the quotient is a whole number, then 4 and 95,506.25 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:

1 382,025
-1 382,025
Keep dividing by the next highest number until you cannot divide anymore.

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

157253537591751852592954139251,2951,4752,0652,1836,47510,32510,91515,28154,57576,405382,025
-1-5-7-25-35-37-59-175-185-259-295-413-925-1,295-1,475-2,065-2,183-6,475-10,325-10,915-15,281-54,575-76,405-382,025

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