Q: What are the factor combinations of the number 420,604,745?

 A:
Positive:   1 x 4206047455 x 8412094911 x 3823679531 x 1356789555 x 7647359155 x 2713579341 x 12334451705 x 246689
Negative: -1 x -420604745-5 x -84120949-11 x -38236795-31 x -13567895-55 x -7647359-155 x -2713579-341 x -1233445-1705 x -246689


How do I find the factor combinations of the number 420,604,745?

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 420,604,745, 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.

1 420,604,745
-1 -420,604,745

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 420,604,745.

Example:
1 x 420,604,745 = 420,604,745
and
-1 x -420,604,745 = 420,604,745
Notice both answers equal 420,604,745

With that explanation out of the way, let's continue. Next, we take the number 420,604,745 and divide it by 2:

420,604,745 ÷ 2 = 210,302,372.5

If the quotient is a whole number, then 2 and 210,302,372.5 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:

1 420,604,745
-1 -420,604,745

Now, we try dividing 420,604,745 by 3:

420,604,745 ÷ 3 = 140,201,581.6667

If the quotient is a whole number, then 3 and 140,201,581.6667 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:

1 420,604,745
-1 -420,604,745

Let's try dividing by 4:

420,604,745 ÷ 4 = 105,151,186.25

If the quotient is a whole number, then 4 and 105,151,186.25 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:

1 420,604,745
-1 420,604,745
Keep dividing by the next highest number until you cannot divide anymore.

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

151131551553411,705246,6891,233,4452,713,5797,647,35913,567,89538,236,79584,120,949420,604,745
-1-5-11-31-55-155-341-1,705-246,689-1,233,445-2,713,579-7,647,359-13,567,895-38,236,795-84,120,949-420,604,745

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