Q: What are the factor combinations of the number 424,015,722?

 A:
Positive:   1 x 4240157222 x 2120078613 x 1413385746 x 706692879 x 4711285813 x 3261659418 x 2355642926 x 1630829727 x 1570428639 x 1087219854 x 785214378 x 543609981 x 5234762117 x 3624066162 x 2617381234 x 1812033351 x 1208022702 x 6040111053 x 4026742106 x 201337
Negative: -1 x -424015722-2 x -212007861-3 x -141338574-6 x -70669287-9 x -47112858-13 x -32616594-18 x -23556429-26 x -16308297-27 x -15704286-39 x -10872198-54 x -7852143-78 x -5436099-81 x -5234762-117 x -3624066-162 x -2617381-234 x -1812033-351 x -1208022-702 x -604011-1053 x -402674-2106 x -201337


How do I find the factor combinations of the number 424,015,722?

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 424,015,722, 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.

1 424,015,722
-1 -424,015,722

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 424,015,722.

Example:
1 x 424,015,722 = 424,015,722
and
-1 x -424,015,722 = 424,015,722
Notice both answers equal 424,015,722

With that explanation out of the way, let's continue. Next, we take the number 424,015,722 and divide it by 2:

424,015,722 ÷ 2 = 212,007,861

If the quotient is a whole number, then 2 and 212,007,861 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 2 212,007,861 424,015,722
-1 -2 -212,007,861 -424,015,722

Now, we try dividing 424,015,722 by 3:

424,015,722 ÷ 3 = 141,338,574

If the quotient is a whole number, then 3 and 141,338,574 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 3 141,338,574 212,007,861 424,015,722
-1 -2 -3 -141,338,574 -212,007,861 -424,015,722

Let's try dividing by 4:

424,015,722 ÷ 4 = 106,003,930.5

If the quotient is a whole number, then 4 and 106,003,930.5 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 3 141,338,574 212,007,861 424,015,722
-1 -2 -3 -141,338,574 -212,007,861 424,015,722
Keep dividing by the next highest number until you cannot divide anymore.

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

1236913182627395478811171622343517021,0532,106201,337402,674604,0111,208,0221,812,0332,617,3813,624,0665,234,7625,436,0997,852,14310,872,19815,704,28616,308,29723,556,42932,616,59447,112,85870,669,287141,338,574212,007,861424,015,722
-1-2-3-6-9-13-18-26-27-39-54-78-81-117-162-234-351-702-1,053-2,106-201,337-402,674-604,011-1,208,022-1,812,033-2,617,381-3,624,066-5,234,762-5,436,099-7,852,143-10,872,198-15,704,286-16,308,297-23,556,429-32,616,594-47,112,858-70,669,287-141,338,574-212,007,861-424,015,722

More Examples

Here are some more numbers to try:

424,015,720424,015,721424,015,723424,015,724
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