Q: What are the factor combinations of the number 738,286,735?

 A:
Positive:   1 x 7382867355 x 14765734767 x 11019205335 x 22038411117 x 6609551973 x 3741955585 x 1321919865 x 74839
Negative: -1 x -738286735-5 x -147657347-67 x -11019205-335 x -2203841-1117 x -660955-1973 x -374195-5585 x -132191-9865 x -74839


How do I find the factor combinations of the number 738,286,735?

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 738,286,735, 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.

1 738,286,735
-1 -738,286,735

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 738,286,735.

Example:
1 x 738,286,735 = 738,286,735
and
-1 x -738,286,735 = 738,286,735
Notice both answers equal 738,286,735

With that explanation out of the way, let's continue. Next, we take the number 738,286,735 and divide it by 2:

738,286,735 ÷ 2 = 369,143,367.5

If the quotient is a whole number, then 2 and 369,143,367.5 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:

1 738,286,735
-1 -738,286,735

Now, we try dividing 738,286,735 by 3:

738,286,735 ÷ 3 = 246,095,578.3333

If the quotient is a whole number, then 3 and 246,095,578.3333 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:

1 738,286,735
-1 -738,286,735

Let's try dividing by 4:

738,286,735 ÷ 4 = 184,571,683.75

If the quotient is a whole number, then 4 and 184,571,683.75 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:

1 738,286,735
-1 738,286,735
Keep dividing by the next highest number until you cannot divide anymore.

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

15673351,1171,9735,5859,86574,839132,191374,195660,9552,203,84111,019,205147,657,347738,286,735
-1-5-67-335-1,117-1,973-5,585-9,865-74,839-132,191-374,195-660,955-2,203,841-11,019,205-147,657,347-738,286,735

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