Q: What are the factor combinations of the number 153,125,123?

 A:
Positive:   1 x 15312512319 x 805921783 x 184488189 x 17205071091 x 1403531577 x 970991691 x 905537387 x 20729
Negative: -1 x -153125123-19 x -8059217-83 x -1844881-89 x -1720507-1091 x -140353-1577 x -97099-1691 x -90553-7387 x -20729


How do I find the factor combinations of the number 153,125,123?

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 153,125,123, 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.

1 153,125,123
-1 -153,125,123

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 153,125,123.

Example:
1 x 153,125,123 = 153,125,123
and
-1 x -153,125,123 = 153,125,123
Notice both answers equal 153,125,123

With that explanation out of the way, let's continue. Next, we take the number 153,125,123 and divide it by 2:

153,125,123 ÷ 2 = 76,562,561.5

If the quotient is a whole number, then 2 and 76,562,561.5 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:

1 153,125,123
-1 -153,125,123

Now, we try dividing 153,125,123 by 3:

153,125,123 ÷ 3 = 51,041,707.6667

If the quotient is a whole number, then 3 and 51,041,707.6667 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:

1 153,125,123
-1 -153,125,123

Let's try dividing by 4:

153,125,123 ÷ 4 = 38,281,280.75

If the quotient is a whole number, then 4 and 38,281,280.75 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:

1 153,125,123
-1 153,125,123
Keep dividing by the next highest number until you cannot divide anymore.

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

11983891,0911,5771,6917,38720,72990,55397,099140,3531,720,5071,844,8818,059,217153,125,123
-1-19-83-89-1,091-1,577-1,691-7,387-20,729-90,553-97,099-140,353-1,720,507-1,844,881-8,059,217-153,125,123

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