Q: What are the factor combinations of the number 734,615?

 A:
Positive:   1 x 7346155 x 1469237 x 10494535 x 20989139 x 5285151 x 4865695 x 1057755 x 973
Negative: -1 x -734615-5 x -146923-7 x -104945-35 x -20989-139 x -5285-151 x -4865-695 x -1057-755 x -973


How do I find the factor combinations of the number 734,615?

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 734,615, 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.

1 734,615
-1 -734,615

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 734,615.

Example:
1 x 734,615 = 734,615
and
-1 x -734,615 = 734,615
Notice both answers equal 734,615

With that explanation out of the way, let's continue. Next, we take the number 734,615 and divide it by 2:

734,615 ÷ 2 = 367,307.5

If the quotient is a whole number, then 2 and 367,307.5 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:

1 734,615
-1 -734,615

Now, we try dividing 734,615 by 3:

734,615 ÷ 3 = 244,871.6667

If the quotient is a whole number, then 3 and 244,871.6667 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:

1 734,615
-1 -734,615

Let's try dividing by 4:

734,615 ÷ 4 = 183,653.75

If the quotient is a whole number, then 4 and 183,653.75 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:

1 734,615
-1 734,615
Keep dividing by the next highest number until you cannot divide anymore.

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

157351391516957559731,0574,8655,28520,989104,945146,923734,615
-1-5-7-35-139-151-695-755-973-1,057-4,865-5,285-20,989-104,945-146,923-734,615

More Examples

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