Q: What are the factor combinations of the number 434,904?

 A:
Positive:   1 x 4349042 x 2174523 x 1449684 x 1087266 x 724848 x 5436312 x 3624224 x 18121
Negative: -1 x -434904-2 x -217452-3 x -144968-4 x -108726-6 x -72484-8 x -54363-12 x -36242-24 x -18121


How do I find the factor combinations of the number 434,904?

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 434,904, 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.

1 434,904
-1 -434,904

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 434,904.

Example:
1 x 434,904 = 434,904
and
-1 x -434,904 = 434,904
Notice both answers equal 434,904

With that explanation out of the way, let's continue. Next, we take the number 434,904 and divide it by 2:

434,904 ÷ 2 = 217,452

If the quotient is a whole number, then 2 and 217,452 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 217,452 434,904
-1 -2 -217,452 -434,904

Now, we try dividing 434,904 by 3:

434,904 ÷ 3 = 144,968

If the quotient is a whole number, then 3 and 144,968 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 144,968 217,452 434,904
-1 -2 -3 -144,968 -217,452 -434,904

Let's try dividing by 4:

434,904 ÷ 4 = 108,726

If the quotient is a whole number, then 4 and 108,726 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 108,726 144,968 217,452 434,904
-1 -2 -3 -4 -108,726 -144,968 -217,452 434,904
Keep dividing by the next highest number until you cannot divide anymore.

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

123468122418,12136,24254,36372,484108,726144,968217,452434,904
-1-2-3-4-6-8-12-24-18,121-36,242-54,363-72,484-108,726-144,968-217,452-434,904

More Examples

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