Q: What are the factor combinations of the number 43,001,329?

 A:
Positive:   1 x 430013297 x 614304723 x 186962389 x 483161161 x 267089623 x 690232047 x 210073001 x 14329
Negative: -1 x -43001329-7 x -6143047-23 x -1869623-89 x -483161-161 x -267089-623 x -69023-2047 x -21007-3001 x -14329


How do I find the factor combinations of the number 43,001,329?

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 43,001,329, 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 43,001,329
-1 -43,001,329

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 43,001,329.

Example:
1 x 43,001,329 = 43,001,329
and
-1 x -43,001,329 = 43,001,329
Notice both answers equal 43,001,329

With that explanation out of the way, let's continue. Next, we take the number 43,001,329 and divide it by 2:

43,001,329 ÷ 2 = 21,500,664.5

If the quotient is a whole number, then 2 and 21,500,664.5 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 43,001,329
-1 -43,001,329

Now, we try dividing 43,001,329 by 3:

43,001,329 ÷ 3 = 14,333,776.3333

If the quotient is a whole number, then 3 and 14,333,776.3333 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 43,001,329
-1 -43,001,329

Let's try dividing by 4:

43,001,329 ÷ 4 = 10,750,332.25

If the quotient is a whole number, then 4 and 10,750,332.25 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 43,001,329
-1 43,001,329
Keep dividing by the next highest number until you cannot divide anymore.

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

1723891616232,0473,00114,32921,00769,023267,089483,1611,869,6236,143,04743,001,329
-1-7-23-89-161-623-2,047-3,001-14,329-21,007-69,023-267,089-483,161-1,869,623-6,143,047-43,001,329

More Examples

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