Q: What are the factor combinations of the number 4,678,315?

 A:
Positive:   1 x 46783155 x 93566317 x 27519523 x 20340585 x 55039115 x 40681391 x 119651955 x 2393
Negative: -1 x -4678315-5 x -935663-17 x -275195-23 x -203405-85 x -55039-115 x -40681-391 x -11965-1955 x -2393


How do I find the factor combinations of the number 4,678,315?

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 4,678,315, 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 4,678,315
-1 -4,678,315

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 4,678,315.

Example:
1 x 4,678,315 = 4,678,315
and
-1 x -4,678,315 = 4,678,315
Notice both answers equal 4,678,315

With that explanation out of the way, let's continue. Next, we take the number 4,678,315 and divide it by 2:

4,678,315 ÷ 2 = 2,339,157.5

If the quotient is a whole number, then 2 and 2,339,157.5 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 4,678,315
-1 -4,678,315

Now, we try dividing 4,678,315 by 3:

4,678,315 ÷ 3 = 1,559,438.3333

If the quotient is a whole number, then 3 and 1,559,438.3333 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 4,678,315
-1 -4,678,315

Let's try dividing by 4:

4,678,315 ÷ 4 = 1,169,578.75

If the quotient is a whole number, then 4 and 1,169,578.75 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 4,678,315
-1 4,678,315
Keep dividing by the next highest number until you cannot divide anymore.

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

151723851153911,9552,39311,96540,68155,039203,405275,195935,6634,678,315
-1-5-17-23-85-115-391-1,955-2,393-11,965-40,681-55,039-203,405-275,195-935,663-4,678,315

More Examples

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