Q: What are the factor combinations of the number 54,505,123?

 A:
Positive:   1 x 5450512329 x 187948743 x 1267561109 x 500047401 x 1359231247 x 437093161 x 172434687 x 11629
Negative: -1 x -54505123-29 x -1879487-43 x -1267561-109 x -500047-401 x -135923-1247 x -43709-3161 x -17243-4687 x -11629


How do I find the factor combinations of the number 54,505,123?

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 54,505,123, 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 54,505,123
-1 -54,505,123

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 54,505,123.

Example:
1 x 54,505,123 = 54,505,123
and
-1 x -54,505,123 = 54,505,123
Notice both answers equal 54,505,123

With that explanation out of the way, let's continue. Next, we take the number 54,505,123 and divide it by 2:

54,505,123 ÷ 2 = 27,252,561.5

If the quotient is a whole number, then 2 and 27,252,561.5 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 54,505,123
-1 -54,505,123

Now, we try dividing 54,505,123 by 3:

54,505,123 ÷ 3 = 18,168,374.3333

If the quotient is a whole number, then 3 and 18,168,374.3333 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 54,505,123
-1 -54,505,123

Let's try dividing by 4:

54,505,123 ÷ 4 = 13,626,280.75

If the quotient is a whole number, then 4 and 13,626,280.75 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 54,505,123
-1 54,505,123
Keep dividing by the next highest number until you cannot divide anymore.

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

129431094011,2473,1614,68711,62917,24343,709135,923500,0471,267,5611,879,48754,505,123
-1-29-43-109-401-1,247-3,161-4,687-11,629-17,243-43,709-135,923-500,047-1,267,561-1,879,487-54,505,123

More Examples

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