Q: What are the factor combinations of the number 462,105,306?

 A:
Positive:   1 x 4621053062 x 2310526533 x 1540351026 x 770175519 x 5134503413 x 3554656218 x 2567251726 x 1777328139 x 1184885478 x 5924427117 x 3949618234 x 1974809677 x 6825781354 x 3412892031 x 2275262917 x 1584184062 x 1137635834 x 792096093 x 758428751 x 528068801 x 5250612186 x 3792117502 x 2640317602 x 26253
Negative: -1 x -462105306-2 x -231052653-3 x -154035102-6 x -77017551-9 x -51345034-13 x -35546562-18 x -25672517-26 x -17773281-39 x -11848854-78 x -5924427-117 x -3949618-234 x -1974809-677 x -682578-1354 x -341289-2031 x -227526-2917 x -158418-4062 x -113763-5834 x -79209-6093 x -75842-8751 x -52806-8801 x -52506-12186 x -37921-17502 x -26403-17602 x -26253


How do I find the factor combinations of the number 462,105,306?

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 462,105,306, 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.

1 462,105,306
-1 -462,105,306

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 462,105,306.

Example:
1 x 462,105,306 = 462,105,306
and
-1 x -462,105,306 = 462,105,306
Notice both answers equal 462,105,306

With that explanation out of the way, let's continue. Next, we take the number 462,105,306 and divide it by 2:

462,105,306 ÷ 2 = 231,052,653

If the quotient is a whole number, then 2 and 231,052,653 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 2 231,052,653 462,105,306
-1 -2 -231,052,653 -462,105,306

Now, we try dividing 462,105,306 by 3:

462,105,306 ÷ 3 = 154,035,102

If the quotient is a whole number, then 3 and 154,035,102 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 3 154,035,102 231,052,653 462,105,306
-1 -2 -3 -154,035,102 -231,052,653 -462,105,306

Let's try dividing by 4:

462,105,306 ÷ 4 = 115,526,326.5

If the quotient is a whole number, then 4 and 115,526,326.5 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 3 154,035,102 231,052,653 462,105,306
-1 -2 -3 -154,035,102 -231,052,653 462,105,306
Keep dividing by the next highest number until you cannot divide anymore.

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

1236913182639781172346771,3542,0312,9174,0625,8346,0938,7518,80112,18617,50217,60226,25326,40337,92152,50652,80675,84279,209113,763158,418227,526341,289682,5781,974,8093,949,6185,924,42711,848,85417,773,28125,672,51735,546,56251,345,03477,017,551154,035,102231,052,653462,105,306
-1-2-3-6-9-13-18-26-39-78-117-234-677-1,354-2,031-2,917-4,062-5,834-6,093-8,751-8,801-12,186-17,502-17,602-26,253-26,403-37,921-52,506-52,806-75,842-79,209-113,763-158,418-227,526-341,289-682,578-1,974,809-3,949,618-5,924,427-11,848,854-17,773,281-25,672,517-35,546,562-51,345,034-77,017,551-154,035,102-231,052,653-462,105,306

More Examples

Here are some more numbers to try:

462,105,304462,105,305462,105,307462,105,308
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