Q: What are the factor combinations of the number 407,495?

 A:
Positive:   1 x 4074955 x 8149911 x 3704531 x 1314555 x 7409155 x 2629239 x 1705341 x 1195
Negative: -1 x -407495-5 x -81499-11 x -37045-31 x -13145-55 x -7409-155 x -2629-239 x -1705-341 x -1195


How do I find the factor combinations of the number 407,495?

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 407,495, 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.

1 407,495
-1 -407,495

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 407,495.

Example:
1 x 407,495 = 407,495
and
-1 x -407,495 = 407,495
Notice both answers equal 407,495

With that explanation out of the way, let's continue. Next, we take the number 407,495 and divide it by 2:

407,495 ÷ 2 = 203,747.5

If the quotient is a whole number, then 2 and 203,747.5 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:

1 407,495
-1 -407,495

Now, we try dividing 407,495 by 3:

407,495 ÷ 3 = 135,831.6667

If the quotient is a whole number, then 3 and 135,831.6667 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:

1 407,495
-1 -407,495

Let's try dividing by 4:

407,495 ÷ 4 = 101,873.75

If the quotient is a whole number, then 4 and 101,873.75 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:

1 407,495
-1 407,495
Keep dividing by the next highest number until you cannot divide anymore.

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

151131551552393411,1951,7052,6297,40913,14537,04581,499407,495
-1-5-11-31-55-155-239-341-1,195-1,705-2,629-7,409-13,145-37,045-81,499-407,495

More Examples

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