Q: What are the factor combinations of the number 153,212,101?

 A:
Positive:   1 x 1532121017 x 218874432141 x 7156110223 x 14987
Negative: -1 x -153212101-7 x -21887443-2141 x -71561-10223 x -14987


How do I find the factor combinations of the number 153,212,101?

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 153,212,101, 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.

1 153,212,101
-1 -153,212,101

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 153,212,101.

Example:
1 x 153,212,101 = 153,212,101
and
-1 x -153,212,101 = 153,212,101
Notice both answers equal 153,212,101

With that explanation out of the way, let's continue. Next, we take the number 153,212,101 and divide it by 2:

153,212,101 ÷ 2 = 76,606,050.5

If the quotient is a whole number, then 2 and 76,606,050.5 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:

1 153,212,101
-1 -153,212,101

Now, we try dividing 153,212,101 by 3:

153,212,101 ÷ 3 = 51,070,700.3333

If the quotient is a whole number, then 3 and 51,070,700.3333 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:

1 153,212,101
-1 -153,212,101

Let's try dividing by 4:

153,212,101 ÷ 4 = 38,303,025.25

If the quotient is a whole number, then 4 and 38,303,025.25 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:

1 153,212,101
-1 153,212,101
Keep dividing by the next highest number until you cannot divide anymore.

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

172,14110,22314,98771,56121,887,443153,212,101
-1-7-2,141-10,223-14,987-71,561-21,887,443-153,212,101

More Examples

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