Q: What are the factor combinations of the number 700,406,875?

 A:
Positive:   1 x 7004068755 x 1400813757 x 10005812525 x 2801627535 x 20011625125 x 5603255175 x 4002325625 x 1120651875 x 8004654375 x 160093
Negative: -1 x -700406875-5 x -140081375-7 x -100058125-25 x -28016275-35 x -20011625-125 x -5603255-175 x -4002325-625 x -1120651-875 x -800465-4375 x -160093


How do I find the factor combinations of the number 700,406,875?

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 700,406,875, 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.

1 700,406,875
-1 -700,406,875

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 700,406,875.

Example:
1 x 700,406,875 = 700,406,875
and
-1 x -700,406,875 = 700,406,875
Notice both answers equal 700,406,875

With that explanation out of the way, let's continue. Next, we take the number 700,406,875 and divide it by 2:

700,406,875 ÷ 2 = 350,203,437.5

If the quotient is a whole number, then 2 and 350,203,437.5 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:

1 700,406,875
-1 -700,406,875

Now, we try dividing 700,406,875 by 3:

700,406,875 ÷ 3 = 233,468,958.3333

If the quotient is a whole number, then 3 and 233,468,958.3333 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:

1 700,406,875
-1 -700,406,875

Let's try dividing by 4:

700,406,875 ÷ 4 = 175,101,718.75

If the quotient is a whole number, then 4 and 175,101,718.75 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:

1 700,406,875
-1 700,406,875
Keep dividing by the next highest number until you cannot divide anymore.

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

15725351251756258754,375160,093800,4651,120,6514,002,3255,603,25520,011,62528,016,275100,058,125140,081,375700,406,875
-1-5-7-25-35-125-175-625-875-4,375-160,093-800,465-1,120,651-4,002,325-5,603,255-20,011,625-28,016,275-100,058,125-140,081,375-700,406,875

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