Q: What are the factor combinations of the number 302,225?

 A:
Positive:   1 x 3022255 x 604457 x 4317511 x 2747525 x 1208935 x 863555 x 549577 x 3925157 x 1925175 x 1727275 x 1099385 x 785
Negative: -1 x -302225-5 x -60445-7 x -43175-11 x -27475-25 x -12089-35 x -8635-55 x -5495-77 x -3925-157 x -1925-175 x -1727-275 x -1099-385 x -785


How do I find the factor combinations of the number 302,225?

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 302,225, 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.

1 302,225
-1 -302,225

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 302,225.

Example:
1 x 302,225 = 302,225
and
-1 x -302,225 = 302,225
Notice both answers equal 302,225

With that explanation out of the way, let's continue. Next, we take the number 302,225 and divide it by 2:

302,225 ÷ 2 = 151,112.5

If the quotient is a whole number, then 2 and 151,112.5 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:

1 302,225
-1 -302,225

Now, we try dividing 302,225 by 3:

302,225 ÷ 3 = 100,741.6667

If the quotient is a whole number, then 3 and 100,741.6667 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:

1 302,225
-1 -302,225

Let's try dividing by 4:

302,225 ÷ 4 = 75,556.25

If the quotient is a whole number, then 4 and 75,556.25 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:

1 302,225
-1 302,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15711253555771571752753857851,0991,7271,9253,9255,4958,63512,08927,47543,17560,445302,225
-1-5-7-11-25-35-55-77-157-175-275-385-785-1,099-1,727-1,925-3,925-5,495-8,635-12,089-27,475-43,175-60,445-302,225

More Examples

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