Q: What are the factor combinations of the number 462,643,865?

 A:
Positive:   1 x 4626438655 x 9252877317 x 2721434585 x 54428691499 x 3086353631 x 1274157495 x 6172718155 x 25483
Negative: -1 x -462643865-5 x -92528773-17 x -27214345-85 x -5442869-1499 x -308635-3631 x -127415-7495 x -61727-18155 x -25483


How do I find the factor combinations of the number 462,643,865?

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 462,643,865, 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.

1 462,643,865
-1 -462,643,865

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 462,643,865.

Example:
1 x 462,643,865 = 462,643,865
and
-1 x -462,643,865 = 462,643,865
Notice both answers equal 462,643,865

With that explanation out of the way, let's continue. Next, we take the number 462,643,865 and divide it by 2:

462,643,865 ÷ 2 = 231,321,932.5

If the quotient is a whole number, then 2 and 231,321,932.5 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:

1 462,643,865
-1 -462,643,865

Now, we try dividing 462,643,865 by 3:

462,643,865 ÷ 3 = 154,214,621.6667

If the quotient is a whole number, then 3 and 154,214,621.6667 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:

1 462,643,865
-1 -462,643,865

Let's try dividing by 4:

462,643,865 ÷ 4 = 115,660,966.25

If the quotient is a whole number, then 4 and 115,660,966.25 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:

1 462,643,865
-1 462,643,865
Keep dividing by the next highest number until you cannot divide anymore.

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

1517851,4993,6317,49518,15525,48361,727127,415308,6355,442,86927,214,34592,528,773462,643,865
-1-5-17-85-1,499-3,631-7,495-18,155-25,483-61,727-127,415-308,635-5,442,869-27,214,345-92,528,773-462,643,865

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