Q: What are the factor combinations of the number 472,675?

 A:
Positive:   1 x 4726755 x 945357 x 6752525 x 1890735 x 1350537 x 1277573 x 6475175 x 2701185 x 2555259 x 1825365 x 1295511 x 925
Negative: -1 x -472675-5 x -94535-7 x -67525-25 x -18907-35 x -13505-37 x -12775-73 x -6475-175 x -2701-185 x -2555-259 x -1825-365 x -1295-511 x -925


How do I find the factor combinations of the number 472,675?

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 472,675, 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.

1 472,675
-1 -472,675

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 472,675.

Example:
1 x 472,675 = 472,675
and
-1 x -472,675 = 472,675
Notice both answers equal 472,675

With that explanation out of the way, let's continue. Next, we take the number 472,675 and divide it by 2:

472,675 ÷ 2 = 236,337.5

If the quotient is a whole number, then 2 and 236,337.5 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:

1 472,675
-1 -472,675

Now, we try dividing 472,675 by 3:

472,675 ÷ 3 = 157,558.3333

If the quotient is a whole number, then 3 and 157,558.3333 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:

1 472,675
-1 -472,675

Let's try dividing by 4:

472,675 ÷ 4 = 118,168.75

If the quotient is a whole number, then 4 and 118,168.75 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:

1 472,675
-1 472,675
Keep dividing by the next highest number until you cannot divide anymore.

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

157253537731751852593655119251,2951,8252,5552,7016,47512,77513,50518,90767,52594,535472,675
-1-5-7-25-35-37-73-175-185-259-365-511-925-1,295-1,825-2,555-2,701-6,475-12,775-13,505-18,907-67,525-94,535-472,675

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