Q: What are the factor combinations of the number 460,358,778?

 A:
Positive:   1 x 4603587782 x 2301793893 x 1534529266 x 7672646311 x 4185079822 x 2092539933 x 1395026666 x 6975133121 x 3804618242 x 1902309363 x 1268206726 x 634103
Negative: -1 x -460358778-2 x -230179389-3 x -153452926-6 x -76726463-11 x -41850798-22 x -20925399-33 x -13950266-66 x -6975133-121 x -3804618-242 x -1902309-363 x -1268206-726 x -634103


How do I find the factor combinations of the number 460,358,778?

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 460,358,778, 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.

1 460,358,778
-1 -460,358,778

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 460,358,778.

Example:
1 x 460,358,778 = 460,358,778
and
-1 x -460,358,778 = 460,358,778
Notice both answers equal 460,358,778

With that explanation out of the way, let's continue. Next, we take the number 460,358,778 and divide it by 2:

460,358,778 ÷ 2 = 230,179,389

If the quotient is a whole number, then 2 and 230,179,389 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 230,179,389 460,358,778
-1 -2 -230,179,389 -460,358,778

Now, we try dividing 460,358,778 by 3:

460,358,778 ÷ 3 = 153,452,926

If the quotient is a whole number, then 3 and 153,452,926 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 153,452,926 230,179,389 460,358,778
-1 -2 -3 -153,452,926 -230,179,389 -460,358,778

Let's try dividing by 4:

460,358,778 ÷ 4 = 115,089,694.5

If the quotient is a whole number, then 4 and 115,089,694.5 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 2 3 153,452,926 230,179,389 460,358,778
-1 -2 -3 -153,452,926 -230,179,389 460,358,778
Keep dividing by the next highest number until you cannot divide anymore.

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

123611223366121242363726634,1031,268,2061,902,3093,804,6186,975,13313,950,26620,925,39941,850,79876,726,463153,452,926230,179,389460,358,778
-1-2-3-6-11-22-33-66-121-242-363-726-634,103-1,268,206-1,902,309-3,804,618-6,975,133-13,950,266-20,925,399-41,850,798-76,726,463-153,452,926-230,179,389-460,358,778

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