Q: What are the factor combinations of the number 472,549?

 A:
Positive:   1 x 4725497 x 6750711 x 4295917 x 2779719 x 2487177 x 6137119 x 3971133 x 3553187 x 2527209 x 2261323 x 1463361 x 1309
Negative: -1 x -472549-7 x -67507-11 x -42959-17 x -27797-19 x -24871-77 x -6137-119 x -3971-133 x -3553-187 x -2527-209 x -2261-323 x -1463-361 x -1309


How do I find the factor combinations of the number 472,549?

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 472,549, 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.

1 472,549
-1 -472,549

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 472,549.

Example:
1 x 472,549 = 472,549
and
-1 x -472,549 = 472,549
Notice both answers equal 472,549

With that explanation out of the way, let's continue. Next, we take the number 472,549 and divide it by 2:

472,549 ÷ 2 = 236,274.5

If the quotient is a whole number, then 2 and 236,274.5 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:

1 472,549
-1 -472,549

Now, we try dividing 472,549 by 3:

472,549 ÷ 3 = 157,516.3333

If the quotient is a whole number, then 3 and 157,516.3333 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:

1 472,549
-1 -472,549

Let's try dividing by 4:

472,549 ÷ 4 = 118,137.25

If the quotient is a whole number, then 4 and 118,137.25 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:

1 472,549
-1 472,549
Keep dividing by the next highest number until you cannot divide anymore.

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

17111719771191331872093233611,3091,4632,2612,5273,5533,9716,13724,87127,79742,95967,507472,549
-1-7-11-17-19-77-119-133-187-209-323-361-1,309-1,463-2,261-2,527-3,553-3,971-6,137-24,871-27,797-42,959-67,507-472,549

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