Q: What are the factor combinations of the number 702,905?

 A:
Positive:   1 x 7029055 x 1405817 x 10041519 x 3699535 x 2008349 x 1434595 x 7399133 x 5285151 x 4655245 x 2869665 x 1057755 x 931
Negative: -1 x -702905-5 x -140581-7 x -100415-19 x -36995-35 x -20083-49 x -14345-95 x -7399-133 x -5285-151 x -4655-245 x -2869-665 x -1057-755 x -931


How do I find the factor combinations of the number 702,905?

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 702,905, 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.

1 702,905
-1 -702,905

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 702,905.

Example:
1 x 702,905 = 702,905
and
-1 x -702,905 = 702,905
Notice both answers equal 702,905

With that explanation out of the way, let's continue. Next, we take the number 702,905 and divide it by 2:

702,905 ÷ 2 = 351,452.5

If the quotient is a whole number, then 2 and 351,452.5 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:

1 702,905
-1 -702,905

Now, we try dividing 702,905 by 3:

702,905 ÷ 3 = 234,301.6667

If the quotient is a whole number, then 3 and 234,301.6667 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:

1 702,905
-1 -702,905

Let's try dividing by 4:

702,905 ÷ 4 = 175,726.25

If the quotient is a whole number, then 4 and 175,726.25 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:

1 702,905
-1 702,905
Keep dividing by the next highest number until you cannot divide anymore.

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

157193549951331512456657559311,0572,8694,6555,2857,39914,34520,08336,995100,415140,581702,905
-1-5-7-19-35-49-95-133-151-245-665-755-931-1,057-2,869-4,655-5,285-7,399-14,345-20,083-36,995-100,415-140,581-702,905

More Examples

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