Q: What are the factor combinations of the number 48,101,105?

 A:
Positive:   1 x 481011055 x 962022113 x 370008565 x 740017499 x 963951483 x 324352495 x 192796487 x 7415
Negative: -1 x -48101105-5 x -9620221-13 x -3700085-65 x -740017-499 x -96395-1483 x -32435-2495 x -19279-6487 x -7415


How do I find the factor combinations of the number 48,101,105?

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 48,101,105, 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 48,101,105
-1 -48,101,105

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 48,101,105.

Example:
1 x 48,101,105 = 48,101,105
and
-1 x -48,101,105 = 48,101,105
Notice both answers equal 48,101,105

With that explanation out of the way, let's continue. Next, we take the number 48,101,105 and divide it by 2:

48,101,105 ÷ 2 = 24,050,552.5

If the quotient is a whole number, then 2 and 24,050,552.5 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 48,101,105
-1 -48,101,105

Now, we try dividing 48,101,105 by 3:

48,101,105 ÷ 3 = 16,033,701.6667

If the quotient is a whole number, then 3 and 16,033,701.6667 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 48,101,105
-1 -48,101,105

Let's try dividing by 4:

48,101,105 ÷ 4 = 12,025,276.25

If the quotient is a whole number, then 4 and 12,025,276.25 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 48,101,105
-1 48,101,105
Keep dividing by the next highest number until you cannot divide anymore.

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

1513654991,4832,4956,4877,41519,27932,43596,395740,0173,700,0859,620,22148,101,105
-1-5-13-65-499-1,483-2,495-6,487-7,415-19,279-32,435-96,395-740,017-3,700,085-9,620,221-48,101,105

More Examples

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