Q: What are the factor combinations of the number 144,150,305?

 A:
Positive:   1 x 1441503055 x 2883006113 x 1108848565 x 22176971093 x 1318852029 x 710455465 x 2637710145 x 14209
Negative: -1 x -144150305-5 x -28830061-13 x -11088485-65 x -2217697-1093 x -131885-2029 x -71045-5465 x -26377-10145 x -14209


How do I find the factor combinations of the number 144,150,305?

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 144,150,305, 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.

1 144,150,305
-1 -144,150,305

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 144,150,305.

Example:
1 x 144,150,305 = 144,150,305
and
-1 x -144,150,305 = 144,150,305
Notice both answers equal 144,150,305

With that explanation out of the way, let's continue. Next, we take the number 144,150,305 and divide it by 2:

144,150,305 ÷ 2 = 72,075,152.5

If the quotient is a whole number, then 2 and 72,075,152.5 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:

1 144,150,305
-1 -144,150,305

Now, we try dividing 144,150,305 by 3:

144,150,305 ÷ 3 = 48,050,101.6667

If the quotient is a whole number, then 3 and 48,050,101.6667 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:

1 144,150,305
-1 -144,150,305

Let's try dividing by 4:

144,150,305 ÷ 4 = 36,037,576.25

If the quotient is a whole number, then 4 and 36,037,576.25 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:

1 144,150,305
-1 144,150,305
Keep dividing by the next highest number until you cannot divide anymore.

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

1513651,0932,0295,46510,14514,20926,37771,045131,8852,217,69711,088,48528,830,061144,150,305
-1-5-13-65-1,093-2,029-5,465-10,145-14,209-26,377-71,045-131,885-2,217,697-11,088,485-28,830,061-144,150,305

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