Q: What are the factor combinations of the number 420,469?

 A:
Positive:   1 x 4204697 x 6006749 x 8581
Negative: -1 x -420469-7 x -60067-49 x -8581


How do I find the factor combinations of the number 420,469?

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 420,469, 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.

1 420,469
-1 -420,469

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 420,469.

Example:
1 x 420,469 = 420,469
and
-1 x -420,469 = 420,469
Notice both answers equal 420,469

With that explanation out of the way, let's continue. Next, we take the number 420,469 and divide it by 2:

420,469 ÷ 2 = 210,234.5

If the quotient is a whole number, then 2 and 210,234.5 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:

1 420,469
-1 -420,469

Now, we try dividing 420,469 by 3:

420,469 ÷ 3 = 140,156.3333

If the quotient is a whole number, then 3 and 140,156.3333 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:

1 420,469
-1 -420,469

Let's try dividing by 4:

420,469 ÷ 4 = 105,117.25

If the quotient is a whole number, then 4 and 105,117.25 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:

1 420,469
-1 420,469
Keep dividing by the next highest number until you cannot divide anymore.

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

17498,58160,067420,469
-1-7-49-8,581-60,067-420,469

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 420,469:


Ask a Question