Q: What are the factor combinations of the number 120,534,541?

 A:
Positive:   1 x 12053454131 x 388821167 x 1799023131 x 920111443 x 2720872077 x 580334061 x 296818777 x 13733
Negative: -1 x -120534541-31 x -3888211-67 x -1799023-131 x -920111-443 x -272087-2077 x -58033-4061 x -29681-8777 x -13733


How do I find the factor combinations of the number 120,534,541?

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 120,534,541, 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.

1 120,534,541
-1 -120,534,541

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 120,534,541.

Example:
1 x 120,534,541 = 120,534,541
and
-1 x -120,534,541 = 120,534,541
Notice both answers equal 120,534,541

With that explanation out of the way, let's continue. Next, we take the number 120,534,541 and divide it by 2:

120,534,541 ÷ 2 = 60,267,270.5

If the quotient is a whole number, then 2 and 60,267,270.5 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:

1 120,534,541
-1 -120,534,541

Now, we try dividing 120,534,541 by 3:

120,534,541 ÷ 3 = 40,178,180.3333

If the quotient is a whole number, then 3 and 40,178,180.3333 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:

1 120,534,541
-1 -120,534,541

Let's try dividing by 4:

120,534,541 ÷ 4 = 30,133,635.25

If the quotient is a whole number, then 4 and 30,133,635.25 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:

1 120,534,541
-1 120,534,541
Keep dividing by the next highest number until you cannot divide anymore.

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

131671314432,0774,0618,77713,73329,68158,033272,087920,1111,799,0233,888,211120,534,541
-1-31-67-131-443-2,077-4,061-8,777-13,733-29,681-58,033-272,087-920,111-1,799,023-3,888,211-120,534,541

More Examples

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