Q: What are the factor combinations of the number 735,324,107?

 A:
Positive:   1 x 7353241077 x 105046301103 x 7139069557 x 1320151721 x 10198671831 x 4015973899 x 18859312817 x 57371
Negative: -1 x -735324107-7 x -105046301-103 x -7139069-557 x -1320151-721 x -1019867-1831 x -401597-3899 x -188593-12817 x -57371


How do I find the factor combinations of the number 735,324,107?

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 735,324,107, 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.

1 735,324,107
-1 -735,324,107

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 735,324,107.

Example:
1 x 735,324,107 = 735,324,107
and
-1 x -735,324,107 = 735,324,107
Notice both answers equal 735,324,107

With that explanation out of the way, let's continue. Next, we take the number 735,324,107 and divide it by 2:

735,324,107 ÷ 2 = 367,662,053.5

If the quotient is a whole number, then 2 and 367,662,053.5 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:

1 735,324,107
-1 -735,324,107

Now, we try dividing 735,324,107 by 3:

735,324,107 ÷ 3 = 245,108,035.6667

If the quotient is a whole number, then 3 and 245,108,035.6667 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:

1 735,324,107
-1 -735,324,107

Let's try dividing by 4:

735,324,107 ÷ 4 = 183,831,026.75

If the quotient is a whole number, then 4 and 183,831,026.75 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:

1 735,324,107
-1 735,324,107
Keep dividing by the next highest number until you cannot divide anymore.

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

171035577211,8313,89912,81757,371188,593401,5971,019,8671,320,1517,139,069105,046,301735,324,107
-1-7-103-557-721-1,831-3,899-12,817-57,371-188,593-401,597-1,019,867-1,320,151-7,139,069-105,046,301-735,324,107

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