Q: What are the factor combinations of the number 45,738,823?

 A:
Positive:   1 x 4573882313 x 351837117 x 269051967 x 682669221 x 206963871 x 525131139 x 401573089 x 14807
Negative: -1 x -45738823-13 x -3518371-17 x -2690519-67 x -682669-221 x -206963-871 x -52513-1139 x -40157-3089 x -14807


How do I find the factor combinations of the number 45,738,823?

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 45,738,823, 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 45,738,823
-1 -45,738,823

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 45,738,823.

Example:
1 x 45,738,823 = 45,738,823
and
-1 x -45,738,823 = 45,738,823
Notice both answers equal 45,738,823

With that explanation out of the way, let's continue. Next, we take the number 45,738,823 and divide it by 2:

45,738,823 ÷ 2 = 22,869,411.5

If the quotient is a whole number, then 2 and 22,869,411.5 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 45,738,823
-1 -45,738,823

Now, we try dividing 45,738,823 by 3:

45,738,823 ÷ 3 = 15,246,274.3333

If the quotient is a whole number, then 3 and 15,246,274.3333 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 45,738,823
-1 -45,738,823

Let's try dividing by 4:

45,738,823 ÷ 4 = 11,434,705.75

If the quotient is a whole number, then 4 and 11,434,705.75 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 45,738,823
-1 45,738,823
Keep dividing by the next highest number until you cannot divide anymore.

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

11317672218711,1393,08914,80740,15752,513206,963682,6692,690,5193,518,37145,738,823
-1-13-17-67-221-871-1,139-3,089-14,807-40,157-52,513-206,963-682,669-2,690,519-3,518,371-45,738,823

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