Q: What are the factor combinations of the number 310,360,645?

 A:
Positive:   1 x 3103606455 x 620721297 x 4433723535 x 88674471847 x 1680354801 x 646459235 x 3360712929 x 24005
Negative: -1 x -310360645-5 x -62072129-7 x -44337235-35 x -8867447-1847 x -168035-4801 x -64645-9235 x -33607-12929 x -24005


How do I find the factor combinations of the number 310,360,645?

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 310,360,645, 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.

1 310,360,645
-1 -310,360,645

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 310,360,645.

Example:
1 x 310,360,645 = 310,360,645
and
-1 x -310,360,645 = 310,360,645
Notice both answers equal 310,360,645

With that explanation out of the way, let's continue. Next, we take the number 310,360,645 and divide it by 2:

310,360,645 ÷ 2 = 155,180,322.5

If the quotient is a whole number, then 2 and 155,180,322.5 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:

1 310,360,645
-1 -310,360,645

Now, we try dividing 310,360,645 by 3:

310,360,645 ÷ 3 = 103,453,548.3333

If the quotient is a whole number, then 3 and 103,453,548.3333 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:

1 310,360,645
-1 -310,360,645

Let's try dividing by 4:

310,360,645 ÷ 4 = 77,590,161.25

If the quotient is a whole number, then 4 and 77,590,161.25 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:

1 310,360,645
-1 310,360,645
Keep dividing by the next highest number until you cannot divide anymore.

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

157351,8474,8019,23512,92924,00533,60764,645168,0358,867,44744,337,23562,072,129310,360,645
-1-5-7-35-1,847-4,801-9,235-12,929-24,005-33,607-64,645-168,035-8,867,447-44,337,235-62,072,129-310,360,645

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