Q: What are the factor combinations of the number 305,045?

 A:
Positive:   1 x 3050455 x 6100913 x 2346519 x 1605565 x 469395 x 3211169 x 1805247 x 1235361 x 845
Negative: -1 x -305045-5 x -61009-13 x -23465-19 x -16055-65 x -4693-95 x -3211-169 x -1805-247 x -1235-361 x -845


How do I find the factor combinations of the number 305,045?

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 305,045, 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.

1 305,045
-1 -305,045

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 305,045.

Example:
1 x 305,045 = 305,045
and
-1 x -305,045 = 305,045
Notice both answers equal 305,045

With that explanation out of the way, let's continue. Next, we take the number 305,045 and divide it by 2:

305,045 ÷ 2 = 152,522.5

If the quotient is a whole number, then 2 and 152,522.5 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:

1 305,045
-1 -305,045

Now, we try dividing 305,045 by 3:

305,045 ÷ 3 = 101,681.6667

If the quotient is a whole number, then 3 and 101,681.6667 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:

1 305,045
-1 -305,045

Let's try dividing by 4:

305,045 ÷ 4 = 76,261.25

If the quotient is a whole number, then 4 and 76,261.25 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:

1 305,045
-1 305,045
Keep dividing by the next highest number until you cannot divide anymore.

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

15131965951692473618451,2351,8053,2114,69316,05523,46561,009305,045
-1-5-13-19-65-95-169-247-361-845-1,235-1,805-3,211-4,693-16,055-23,465-61,009-305,045

More Examples

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