Q: What are the factor combinations of the number 478,225?

 A:
Positive:   1 x 4782255 x 9564511 x 4347525 x 1912937 x 1292547 x 1017555 x 8695185 x 2585235 x 2035275 x 1739407 x 1175517 x 925
Negative: -1 x -478225-5 x -95645-11 x -43475-25 x -19129-37 x -12925-47 x -10175-55 x -8695-185 x -2585-235 x -2035-275 x -1739-407 x -1175-517 x -925


How do I find the factor combinations of the number 478,225?

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 478,225, 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.

1 478,225
-1 -478,225

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 478,225.

Example:
1 x 478,225 = 478,225
and
-1 x -478,225 = 478,225
Notice both answers equal 478,225

With that explanation out of the way, let's continue. Next, we take the number 478,225 and divide it by 2:

478,225 ÷ 2 = 239,112.5

If the quotient is a whole number, then 2 and 239,112.5 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:

1 478,225
-1 -478,225

Now, we try dividing 478,225 by 3:

478,225 ÷ 3 = 159,408.3333

If the quotient is a whole number, then 3 and 159,408.3333 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:

1 478,225
-1 -478,225

Let's try dividing by 4:

478,225 ÷ 4 = 119,556.25

If the quotient is a whole number, then 4 and 119,556.25 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:

1 478,225
-1 478,225
Keep dividing by the next highest number until you cannot divide anymore.

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

1511253747551852352754075179251,1751,7392,0352,5858,69510,17512,92519,12943,47595,645478,225
-1-5-11-25-37-47-55-185-235-275-407-517-925-1,175-1,739-2,035-2,585-8,695-10,175-12,925-19,129-43,475-95,645-478,225

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