Q: What are the factor combinations of the number 136,465?

 A:
Positive:   1 x 1364655 x 272937 x 1949535 x 389949 x 2785245 x 557
Negative: -1 x -136465-5 x -27293-7 x -19495-35 x -3899-49 x -2785-245 x -557


How do I find the factor combinations of the number 136,465?

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 136,465, 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.

1 136,465
-1 -136,465

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 136,465.

Example:
1 x 136,465 = 136,465
and
-1 x -136,465 = 136,465
Notice both answers equal 136,465

With that explanation out of the way, let's continue. Next, we take the number 136,465 and divide it by 2:

136,465 ÷ 2 = 68,232.5

If the quotient is a whole number, then 2 and 68,232.5 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:

1 136,465
-1 -136,465

Now, we try dividing 136,465 by 3:

136,465 ÷ 3 = 45,488.3333

If the quotient is a whole number, then 3 and 45,488.3333 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:

1 136,465
-1 -136,465

Let's try dividing by 4:

136,465 ÷ 4 = 34,116.25

If the quotient is a whole number, then 4 and 34,116.25 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:

1 136,465
-1 136,465
Keep dividing by the next highest number until you cannot divide anymore.

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

15735492455572,7853,89919,49527,293136,465
-1-5-7-35-49-245-557-2,785-3,899-19,495-27,293-136,465

More Examples

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