Q: What are the factor combinations of the number 308,275?

 A:
Positive:   1 x 3082755 x 6165511 x 2802519 x 1622525 x 1233155 x 560559 x 522595 x 3245209 x 1475275 x 1121295 x 1045475 x 649
Negative: -1 x -308275-5 x -61655-11 x -28025-19 x -16225-25 x -12331-55 x -5605-59 x -5225-95 x -3245-209 x -1475-275 x -1121-295 x -1045-475 x -649


How do I find the factor combinations of the number 308,275?

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 308,275, 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.

1 308,275
-1 -308,275

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 308,275.

Example:
1 x 308,275 = 308,275
and
-1 x -308,275 = 308,275
Notice both answers equal 308,275

With that explanation out of the way, let's continue. Next, we take the number 308,275 and divide it by 2:

308,275 ÷ 2 = 154,137.5

If the quotient is a whole number, then 2 and 154,137.5 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:

1 308,275
-1 -308,275

Now, we try dividing 308,275 by 3:

308,275 ÷ 3 = 102,758.3333

If the quotient is a whole number, then 3 and 102,758.3333 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:

1 308,275
-1 -308,275

Let's try dividing by 4:

308,275 ÷ 4 = 77,068.75

If the quotient is a whole number, then 4 and 77,068.75 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:

1 308,275
-1 308,275
Keep dividing by the next highest number until you cannot divide anymore.

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

151119255559952092752954756491,0451,1211,4753,2455,2255,60512,33116,22528,02561,655308,275
-1-5-11-19-25-55-59-95-209-275-295-475-649-1,045-1,121-1,475-3,245-5,225-5,605-12,331-16,225-28,025-61,655-308,275

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