Q: What are the factor combinations of the number 362,394,835?

 A:
Positive:   1 x 3623948355 x 7247896711 x 3294498537 x 979445555 x 6588997185 x 1958891407 x 8904051369 x 2647152035 x 1780814813 x 752956845 x 5294315059 x 24065
Negative: -1 x -362394835-5 x -72478967-11 x -32944985-37 x -9794455-55 x -6588997-185 x -1958891-407 x -890405-1369 x -264715-2035 x -178081-4813 x -75295-6845 x -52943-15059 x -24065


How do I find the factor combinations of the number 362,394,835?

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 362,394,835, 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.

1 362,394,835
-1 -362,394,835

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 362,394,835.

Example:
1 x 362,394,835 = 362,394,835
and
-1 x -362,394,835 = 362,394,835
Notice both answers equal 362,394,835

With that explanation out of the way, let's continue. Next, we take the number 362,394,835 and divide it by 2:

362,394,835 ÷ 2 = 181,197,417.5

If the quotient is a whole number, then 2 and 181,197,417.5 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:

1 362,394,835
-1 -362,394,835

Now, we try dividing 362,394,835 by 3:

362,394,835 ÷ 3 = 120,798,278.3333

If the quotient is a whole number, then 3 and 120,798,278.3333 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:

1 362,394,835
-1 -362,394,835

Let's try dividing by 4:

362,394,835 ÷ 4 = 90,598,708.75

If the quotient is a whole number, then 4 and 90,598,708.75 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:

1 362,394,835
-1 362,394,835
Keep dividing by the next highest number until you cannot divide anymore.

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

151137551854071,3692,0354,8136,84515,05924,06552,94375,295178,081264,715890,4051,958,8916,588,9979,794,45532,944,98572,478,967362,394,835
-1-5-11-37-55-185-407-1,369-2,035-4,813-6,845-15,059-24,065-52,943-75,295-178,081-264,715-890,405-1,958,891-6,588,997-9,794,455-32,944,985-72,478,967-362,394,835

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