Q: What are the factor combinations of the number 44,102,431?

 A:
Positive:   1 x 4410243123 x 191749771 x 621161113 x 390287239 x 1845291633 x 270072599 x 169695497 x 8023
Negative: -1 x -44102431-23 x -1917497-71 x -621161-113 x -390287-239 x -184529-1633 x -27007-2599 x -16969-5497 x -8023


How do I find the factor combinations of the number 44,102,431?

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 44,102,431, 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 44,102,431
-1 -44,102,431

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 44,102,431.

Example:
1 x 44,102,431 = 44,102,431
and
-1 x -44,102,431 = 44,102,431
Notice both answers equal 44,102,431

With that explanation out of the way, let's continue. Next, we take the number 44,102,431 and divide it by 2:

44,102,431 ÷ 2 = 22,051,215.5

If the quotient is a whole number, then 2 and 22,051,215.5 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 44,102,431
-1 -44,102,431

Now, we try dividing 44,102,431 by 3:

44,102,431 ÷ 3 = 14,700,810.3333

If the quotient is a whole number, then 3 and 14,700,810.3333 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 44,102,431
-1 -44,102,431

Let's try dividing by 4:

44,102,431 ÷ 4 = 11,025,607.75

If the quotient is a whole number, then 4 and 11,025,607.75 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 44,102,431
-1 44,102,431
Keep dividing by the next highest number until you cannot divide anymore.

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

123711132391,6332,5995,4978,02316,96927,007184,529390,287621,1611,917,49744,102,431
-1-23-71-113-239-1,633-2,599-5,497-8,023-16,969-27,007-184,529-390,287-621,161-1,917,497-44,102,431

More Examples

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