Q: What are the factor combinations of the number 362,425?

 A:
Positive:   1 x 3624255 x 724857 x 5177519 x 1907525 x 1449735 x 1035595 x 3815109 x 3325133 x 2725175 x 2071475 x 763545 x 665
Negative: -1 x -362425-5 x -72485-7 x -51775-19 x -19075-25 x -14497-35 x -10355-95 x -3815-109 x -3325-133 x -2725-175 x -2071-475 x -763-545 x -665


How do I find the factor combinations of the number 362,425?

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 362,425, 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.

1 362,425
-1 -362,425

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 362,425.

Example:
1 x 362,425 = 362,425
and
-1 x -362,425 = 362,425
Notice both answers equal 362,425

With that explanation out of the way, let's continue. Next, we take the number 362,425 and divide it by 2:

362,425 ÷ 2 = 181,212.5

If the quotient is a whole number, then 2 and 181,212.5 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:

1 362,425
-1 -362,425

Now, we try dividing 362,425 by 3:

362,425 ÷ 3 = 120,808.3333

If the quotient is a whole number, then 3 and 120,808.3333 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:

1 362,425
-1 -362,425

Let's try dividing by 4:

362,425 ÷ 4 = 90,606.25

If the quotient is a whole number, then 4 and 90,606.25 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:

1 362,425
-1 362,425
Keep dividing by the next highest number until you cannot divide anymore.

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

157192535951091331754755456657632,0712,7253,3253,81510,35514,49719,07551,77572,485362,425
-1-5-7-19-25-35-95-109-133-175-475-545-665-763-2,071-2,725-3,325-3,815-10,355-14,497-19,075-51,775-72,485-362,425

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