Q: What are the factor combinations of the number 423,775?

 A:
Positive:   1 x 4237755 x 8475511 x 3852523 x 1842525 x 1695155 x 770567 x 6325115 x 3685253 x 1675275 x 1541335 x 1265575 x 737
Negative: -1 x -423775-5 x -84755-11 x -38525-23 x -18425-25 x -16951-55 x -7705-67 x -6325-115 x -3685-253 x -1675-275 x -1541-335 x -1265-575 x -737


How do I find the factor combinations of the number 423,775?

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 423,775, 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.

1 423,775
-1 -423,775

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 423,775.

Example:
1 x 423,775 = 423,775
and
-1 x -423,775 = 423,775
Notice both answers equal 423,775

With that explanation out of the way, let's continue. Next, we take the number 423,775 and divide it by 2:

423,775 ÷ 2 = 211,887.5

If the quotient is a whole number, then 2 and 211,887.5 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:

1 423,775
-1 -423,775

Now, we try dividing 423,775 by 3:

423,775 ÷ 3 = 141,258.3333

If the quotient is a whole number, then 3 and 141,258.3333 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:

1 423,775
-1 -423,775

Let's try dividing by 4:

423,775 ÷ 4 = 105,943.75

If the quotient is a whole number, then 4 and 105,943.75 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:

1 423,775
-1 423,775
Keep dividing by the next highest number until you cannot divide anymore.

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

1511232555671152532753355757371,2651,5411,6753,6856,3257,70516,95118,42538,52584,755423,775
-1-5-11-23-25-55-67-115-253-275-335-575-737-1,265-1,541-1,675-3,685-6,325-7,705-16,951-18,425-38,525-84,755-423,775

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