Q: What are the factor combinations of the number 12,035,023?

 A:
Positive:   1 x 120350237 x 171928911 x 109409313 x 92577177 x 15629991 x 132253121 x 99463143 x 84161847 x 142091001 x 120231093 x 110111573 x 7651
Negative: -1 x -12035023-7 x -1719289-11 x -1094093-13 x -925771-77 x -156299-91 x -132253-121 x -99463-143 x -84161-847 x -14209-1001 x -12023-1093 x -11011-1573 x -7651


How do I find the factor combinations of the number 12,035,023?

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 12,035,023, 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 12,035,023
-1 -12,035,023

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 12,035,023.

Example:
1 x 12,035,023 = 12,035,023
and
-1 x -12,035,023 = 12,035,023
Notice both answers equal 12,035,023

With that explanation out of the way, let's continue. Next, we take the number 12,035,023 and divide it by 2:

12,035,023 ÷ 2 = 6,017,511.5

If the quotient is a whole number, then 2 and 6,017,511.5 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 12,035,023
-1 -12,035,023

Now, we try dividing 12,035,023 by 3:

12,035,023 ÷ 3 = 4,011,674.3333

If the quotient is a whole number, then 3 and 4,011,674.3333 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 12,035,023
-1 -12,035,023

Let's try dividing by 4:

12,035,023 ÷ 4 = 3,008,755.75

If the quotient is a whole number, then 4 and 3,008,755.75 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 12,035,023
-1 12,035,023
Keep dividing by the next highest number until you cannot divide anymore.

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

17111377911211438471,0011,0931,5737,65111,01112,02314,20984,16199,463132,253156,299925,7711,094,0931,719,28912,035,023
-1-7-11-13-77-91-121-143-847-1,001-1,093-1,573-7,651-11,011-12,023-14,209-84,161-99,463-132,253-156,299-925,771-1,094,093-1,719,289-12,035,023

More Examples

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