Q: What are the factor combinations of the number 434,310,365?

 A:
Positive:   1 x 4343103655 x 8686207383 x 5232655139 x 3124535415 x 1046531695 x 6249077529 x 5768511537 x 37645
Negative: -1 x -434310365-5 x -86862073-83 x -5232655-139 x -3124535-415 x -1046531-695 x -624907-7529 x -57685-11537 x -37645


How do I find the factor combinations of the number 434,310,365?

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 434,310,365, 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.

1 434,310,365
-1 -434,310,365

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 434,310,365.

Example:
1 x 434,310,365 = 434,310,365
and
-1 x -434,310,365 = 434,310,365
Notice both answers equal 434,310,365

With that explanation out of the way, let's continue. Next, we take the number 434,310,365 and divide it by 2:

434,310,365 ÷ 2 = 217,155,182.5

If the quotient is a whole number, then 2 and 217,155,182.5 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:

1 434,310,365
-1 -434,310,365

Now, we try dividing 434,310,365 by 3:

434,310,365 ÷ 3 = 144,770,121.6667

If the quotient is a whole number, then 3 and 144,770,121.6667 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:

1 434,310,365
-1 -434,310,365

Let's try dividing by 4:

434,310,365 ÷ 4 = 108,577,591.25

If the quotient is a whole number, then 4 and 108,577,591.25 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:

1 434,310,365
-1 434,310,365
Keep dividing by the next highest number until you cannot divide anymore.

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

15831394156957,52911,53737,64557,685624,9071,046,5313,124,5355,232,65586,862,073434,310,365
-1-5-83-139-415-695-7,529-11,537-37,645-57,685-624,907-1,046,531-3,124,535-5,232,655-86,862,073-434,310,365

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