Q: What are the factor combinations of the number 144,123,241?

 A:
Positive:   1 x 14412324141 x 3515201181 x 7962617421 x 19421
Negative: -1 x -144123241-41 x -3515201-181 x -796261-7421 x -19421


How do I find the factor combinations of the number 144,123,241?

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 144,123,241, 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.

1 144,123,241
-1 -144,123,241

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 144,123,241.

Example:
1 x 144,123,241 = 144,123,241
and
-1 x -144,123,241 = 144,123,241
Notice both answers equal 144,123,241

With that explanation out of the way, let's continue. Next, we take the number 144,123,241 and divide it by 2:

144,123,241 ÷ 2 = 72,061,620.5

If the quotient is a whole number, then 2 and 72,061,620.5 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:

1 144,123,241
-1 -144,123,241

Now, we try dividing 144,123,241 by 3:

144,123,241 ÷ 3 = 48,041,080.3333

If the quotient is a whole number, then 3 and 48,041,080.3333 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:

1 144,123,241
-1 -144,123,241

Let's try dividing by 4:

144,123,241 ÷ 4 = 36,030,810.25

If the quotient is a whole number, then 4 and 36,030,810.25 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:

1 144,123,241
-1 144,123,241
Keep dividing by the next highest number until you cannot divide anymore.

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

1411817,42119,421796,2613,515,201144,123,241
-1-41-181-7,421-19,421-796,261-3,515,201-144,123,241

More Examples

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