Q: What are the factor combinations of the number 4,612,321?

 A:
Positive:   1 x 46123217 x 65890317 x 27131349 x 94129113 x 40817119 x 38759343 x 13447791 x 5831833 x 55371921 x 2401
Negative: -1 x -4612321-7 x -658903-17 x -271313-49 x -94129-113 x -40817-119 x -38759-343 x -13447-791 x -5831-833 x -5537-1921 x -2401


How do I find the factor combinations of the number 4,612,321?

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 4,612,321, 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 4,612,321
-1 -4,612,321

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 4,612,321.

Example:
1 x 4,612,321 = 4,612,321
and
-1 x -4,612,321 = 4,612,321
Notice both answers equal 4,612,321

With that explanation out of the way, let's continue. Next, we take the number 4,612,321 and divide it by 2:

4,612,321 ÷ 2 = 2,306,160.5

If the quotient is a whole number, then 2 and 2,306,160.5 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 4,612,321
-1 -4,612,321

Now, we try dividing 4,612,321 by 3:

4,612,321 ÷ 3 = 1,537,440.3333

If the quotient is a whole number, then 3 and 1,537,440.3333 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 4,612,321
-1 -4,612,321

Let's try dividing by 4:

4,612,321 ÷ 4 = 1,153,080.25

If the quotient is a whole number, then 4 and 1,153,080.25 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 4,612,321
-1 4,612,321
Keep dividing by the next highest number until you cannot divide anymore.

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

1717491131193437918331,9212,4015,5375,83113,44738,75940,81794,129271,313658,9034,612,321
-1-7-17-49-113-119-343-791-833-1,921-2,401-5,537-5,831-13,447-38,759-40,817-94,129-271,313-658,903-4,612,321

More Examples

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