Q: What are the factor combinations of the number 144,541,441?

 A:
Positive:   1 x 14454144111 x 1314013141 x 352540153 x 2727197451 x 320491583 x 2479272173 x 665176047 x 23903
Negative: -1 x -144541441-11 x -13140131-41 x -3525401-53 x -2727197-451 x -320491-583 x -247927-2173 x -66517-6047 x -23903


How do I find the factor combinations of the number 144,541,441?

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 144,541,441, 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.

1 144,541,441
-1 -144,541,441

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 144,541,441.

Example:
1 x 144,541,441 = 144,541,441
and
-1 x -144,541,441 = 144,541,441
Notice both answers equal 144,541,441

With that explanation out of the way, let's continue. Next, we take the number 144,541,441 and divide it by 2:

144,541,441 ÷ 2 = 72,270,720.5

If the quotient is a whole number, then 2 and 72,270,720.5 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:

1 144,541,441
-1 -144,541,441

Now, we try dividing 144,541,441 by 3:

144,541,441 ÷ 3 = 48,180,480.3333

If the quotient is a whole number, then 3 and 48,180,480.3333 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:

1 144,541,441
-1 -144,541,441

Let's try dividing by 4:

144,541,441 ÷ 4 = 36,135,360.25

If the quotient is a whole number, then 4 and 36,135,360.25 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:

1 144,541,441
-1 144,541,441
Keep dividing by the next highest number until you cannot divide anymore.

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

11141534515832,1736,04723,90366,517247,927320,4912,727,1973,525,40113,140,131144,541,441
-1-11-41-53-451-583-2,173-6,047-23,903-66,517-247,927-320,491-2,727,197-3,525,401-13,140,131-144,541,441

More Examples

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