Q: What are the factor combinations of the number 144,305?

 A:
Positive:   1 x 1443055 x 288617 x 2061519 x 759531 x 465535 x 412349 x 294595 x 1519133 x 1085155 x 931217 x 665245 x 589
Negative: -1 x -144305-5 x -28861-7 x -20615-19 x -7595-31 x -4655-35 x -4123-49 x -2945-95 x -1519-133 x -1085-155 x -931-217 x -665-245 x -589


How do I find the factor combinations of the number 144,305?

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 144,305, 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.

1 144,305
-1 -144,305

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 144,305.

Example:
1 x 144,305 = 144,305
and
-1 x -144,305 = 144,305
Notice both answers equal 144,305

With that explanation out of the way, let's continue. Next, we take the number 144,305 and divide it by 2:

144,305 ÷ 2 = 72,152.5

If the quotient is a whole number, then 2 and 72,152.5 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:

1 144,305
-1 -144,305

Now, we try dividing 144,305 by 3:

144,305 ÷ 3 = 48,101.6667

If the quotient is a whole number, then 3 and 48,101.6667 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:

1 144,305
-1 -144,305

Let's try dividing by 4:

144,305 ÷ 4 = 36,076.25

If the quotient is a whole number, then 4 and 36,076.25 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:

1 144,305
-1 144,305
Keep dividing by the next highest number until you cannot divide anymore.

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

15719313549951331552172455896659311,0851,5192,9454,1234,6557,59520,61528,861144,305
-1-5-7-19-31-35-49-95-133-155-217-245-589-665-931-1,085-1,519-2,945-4,123-4,655-7,595-20,615-28,861-144,305

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