Q: What are the factor combinations of the number 43,824,017?

 A:
Positive:   1 x 4382401729 x 151117373 x 600329127 x 345071163 x 2688592117 x 207013683 x 118994727 x 9271
Negative: -1 x -43824017-29 x -1511173-73 x -600329-127 x -345071-163 x -268859-2117 x -20701-3683 x -11899-4727 x -9271


How do I find the factor combinations of the number 43,824,017?

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 43,824,017, 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 43,824,017
-1 -43,824,017

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 43,824,017.

Example:
1 x 43,824,017 = 43,824,017
and
-1 x -43,824,017 = 43,824,017
Notice both answers equal 43,824,017

With that explanation out of the way, let's continue. Next, we take the number 43,824,017 and divide it by 2:

43,824,017 ÷ 2 = 21,912,008.5

If the quotient is a whole number, then 2 and 21,912,008.5 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 43,824,017
-1 -43,824,017

Now, we try dividing 43,824,017 by 3:

43,824,017 ÷ 3 = 14,608,005.6667

If the quotient is a whole number, then 3 and 14,608,005.6667 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 43,824,017
-1 -43,824,017

Let's try dividing by 4:

43,824,017 ÷ 4 = 10,956,004.25

If the quotient is a whole number, then 4 and 10,956,004.25 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 43,824,017
-1 43,824,017
Keep dividing by the next highest number until you cannot divide anymore.

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

129731271632,1173,6834,7279,27111,89920,701268,859345,071600,3291,511,17343,824,017
-1-29-73-127-163-2,117-3,683-4,727-9,271-11,899-20,701-268,859-345,071-600,329-1,511,173-43,824,017

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