Q: What are the factor combinations of the number 5,214,223?

 A:
Positive:   1 x 52142237 x 74488917 x 30671943 x 121261119 x 43817301 x 17323731 x 71331019 x 5117
Negative: -1 x -5214223-7 x -744889-17 x -306719-43 x -121261-119 x -43817-301 x -17323-731 x -7133-1019 x -5117


How do I find the factor combinations of the number 5,214,223?

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 5,214,223, 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 5,214,223
-1 -5,214,223

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 5,214,223.

Example:
1 x 5,214,223 = 5,214,223
and
-1 x -5,214,223 = 5,214,223
Notice both answers equal 5,214,223

With that explanation out of the way, let's continue. Next, we take the number 5,214,223 and divide it by 2:

5,214,223 ÷ 2 = 2,607,111.5

If the quotient is a whole number, then 2 and 2,607,111.5 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 5,214,223
-1 -5,214,223

Now, we try dividing 5,214,223 by 3:

5,214,223 ÷ 3 = 1,738,074.3333

If the quotient is a whole number, then 3 and 1,738,074.3333 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 5,214,223
-1 -5,214,223

Let's try dividing by 4:

5,214,223 ÷ 4 = 1,303,555.75

If the quotient is a whole number, then 4 and 1,303,555.75 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 5,214,223
-1 5,214,223
Keep dividing by the next highest number until you cannot divide anymore.

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

1717431193017311,0195,1177,13317,32343,817121,261306,719744,8895,214,223
-1-7-17-43-119-301-731-1,019-5,117-7,133-17,323-43,817-121,261-306,719-744,889-5,214,223

More Examples

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