Q: What are the factor combinations of the number 460,723,835?

 A:
Positive:   1 x 4607238355 x 9214476711 x 4188398513 x 3544029555 x 837679765 x 7088059121 x 3807635143 x 3221845605 x 761527715 x 6443691573 x 2928957865 x 58579
Negative: -1 x -460723835-5 x -92144767-11 x -41883985-13 x -35440295-55 x -8376797-65 x -7088059-121 x -3807635-143 x -3221845-605 x -761527-715 x -644369-1573 x -292895-7865 x -58579


How do I find the factor combinations of the number 460,723,835?

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 460,723,835, 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.

1 460,723,835
-1 -460,723,835

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 460,723,835.

Example:
1 x 460,723,835 = 460,723,835
and
-1 x -460,723,835 = 460,723,835
Notice both answers equal 460,723,835

With that explanation out of the way, let's continue. Next, we take the number 460,723,835 and divide it by 2:

460,723,835 ÷ 2 = 230,361,917.5

If the quotient is a whole number, then 2 and 230,361,917.5 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:

1 460,723,835
-1 -460,723,835

Now, we try dividing 460,723,835 by 3:

460,723,835 ÷ 3 = 153,574,611.6667

If the quotient is a whole number, then 3 and 153,574,611.6667 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:

1 460,723,835
-1 -460,723,835

Let's try dividing by 4:

460,723,835 ÷ 4 = 115,180,958.75

If the quotient is a whole number, then 4 and 115,180,958.75 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:

1 460,723,835
-1 460,723,835
Keep dividing by the next highest number until you cannot divide anymore.

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

15111355651211436057151,5737,86558,579292,895644,369761,5273,221,8453,807,6357,088,0598,376,79735,440,29541,883,98592,144,767460,723,835
-1-5-11-13-55-65-121-143-605-715-1,573-7,865-58,579-292,895-644,369-761,527-3,221,845-3,807,635-7,088,059-8,376,797-35,440,295-41,883,985-92,144,767-460,723,835

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