Q: What are the factor combinations of the number 460,915?

 A:
Positive:   1 x 4609155 x 921837 x 6584513 x 3545535 x 1316965 x 709191 x 5065455 x 1013
Negative: -1 x -460915-5 x -92183-7 x -65845-13 x -35455-35 x -13169-65 x -7091-91 x -5065-455 x -1013


How do I find the factor combinations of the number 460,915?

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 460,915, 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.

1 460,915
-1 -460,915

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 460,915.

Example:
1 x 460,915 = 460,915
and
-1 x -460,915 = 460,915
Notice both answers equal 460,915

With that explanation out of the way, let's continue. Next, we take the number 460,915 and divide it by 2:

460,915 ÷ 2 = 230,457.5

If the quotient is a whole number, then 2 and 230,457.5 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:

1 460,915
-1 -460,915

Now, we try dividing 460,915 by 3:

460,915 ÷ 3 = 153,638.3333

If the quotient is a whole number, then 3 and 153,638.3333 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:

1 460,915
-1 -460,915

Let's try dividing by 4:

460,915 ÷ 4 = 115,228.75

If the quotient is a whole number, then 4 and 115,228.75 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:

1 460,915
-1 460,915
Keep dividing by the next highest number until you cannot divide anymore.

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

157133565914551,0135,0657,09113,16935,45565,84592,183460,915
-1-5-7-13-35-65-91-455-1,013-5,065-7,091-13,169-35,455-65,845-92,183-460,915

More Examples

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