Q: What are the factor combinations of the number 362,314,139?

 A:
Positive:   1 x 36231413911 x 3293764929 x 12493591103 x 3517613319 x 11357811133 x 3197832987 x 12129711027 x 32857
Negative: -1 x -362314139-11 x -32937649-29 x -12493591-103 x -3517613-319 x -1135781-1133 x -319783-2987 x -121297-11027 x -32857


How do I find the factor combinations of the number 362,314,139?

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 362,314,139, 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.

1 362,314,139
-1 -362,314,139

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 362,314,139.

Example:
1 x 362,314,139 = 362,314,139
and
-1 x -362,314,139 = 362,314,139
Notice both answers equal 362,314,139

With that explanation out of the way, let's continue. Next, we take the number 362,314,139 and divide it by 2:

362,314,139 ÷ 2 = 181,157,069.5

If the quotient is a whole number, then 2 and 181,157,069.5 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:

1 362,314,139
-1 -362,314,139

Now, we try dividing 362,314,139 by 3:

362,314,139 ÷ 3 = 120,771,379.6667

If the quotient is a whole number, then 3 and 120,771,379.6667 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:

1 362,314,139
-1 -362,314,139

Let's try dividing by 4:

362,314,139 ÷ 4 = 90,578,534.75

If the quotient is a whole number, then 4 and 90,578,534.75 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:

1 362,314,139
-1 362,314,139
Keep dividing by the next highest number until you cannot divide anymore.

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

111291033191,1332,98711,02732,857121,297319,7831,135,7813,517,61312,493,59132,937,649362,314,139
-1-11-29-103-319-1,133-2,987-11,027-32,857-121,297-319,783-1,135,781-3,517,613-12,493,591-32,937,649-362,314,139

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