Q: What are the factor combinations of the number 13,321,105?

 A:
Positive:   1 x 133211055 x 26642217 x 190301535 x 38060341 x 324905205 x 64981287 x 464151435 x 9283
Negative: -1 x -13321105-5 x -2664221-7 x -1903015-35 x -380603-41 x -324905-205 x -64981-287 x -46415-1435 x -9283


How do I find the factor combinations of the number 13,321,105?

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 13,321,105, 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 13,321,105
-1 -13,321,105

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 13,321,105.

Example:
1 x 13,321,105 = 13,321,105
and
-1 x -13,321,105 = 13,321,105
Notice both answers equal 13,321,105

With that explanation out of the way, let's continue. Next, we take the number 13,321,105 and divide it by 2:

13,321,105 ÷ 2 = 6,660,552.5

If the quotient is a whole number, then 2 and 6,660,552.5 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 13,321,105
-1 -13,321,105

Now, we try dividing 13,321,105 by 3:

13,321,105 ÷ 3 = 4,440,368.3333

If the quotient is a whole number, then 3 and 4,440,368.3333 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 13,321,105
-1 -13,321,105

Let's try dividing by 4:

13,321,105 ÷ 4 = 3,330,276.25

If the quotient is a whole number, then 4 and 3,330,276.25 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 13,321,105
-1 13,321,105
Keep dividing by the next highest number until you cannot divide anymore.

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

15735412052871,4359,28346,41564,981324,905380,6031,903,0152,664,22113,321,105
-1-5-7-35-41-205-287-1,435-9,283-46,415-64,981-324,905-380,603-1,903,015-2,664,221-13,321,105

More Examples

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