Q: What are the factor combinations of the number 33,100,145?

 A:
Positive:   1 x 331001455 x 662002913 x 254616565 x 509233241 x 1373451205 x 274692113 x 156653133 x 10565
Negative: -1 x -33100145-5 x -6620029-13 x -2546165-65 x -509233-241 x -137345-1205 x -27469-2113 x -15665-3133 x -10565


How do I find the factor combinations of the number 33,100,145?

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 33,100,145, 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 33,100,145
-1 -33,100,145

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 33,100,145.

Example:
1 x 33,100,145 = 33,100,145
and
-1 x -33,100,145 = 33,100,145
Notice both answers equal 33,100,145

With that explanation out of the way, let's continue. Next, we take the number 33,100,145 and divide it by 2:

33,100,145 ÷ 2 = 16,550,072.5

If the quotient is a whole number, then 2 and 16,550,072.5 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 33,100,145
-1 -33,100,145

Now, we try dividing 33,100,145 by 3:

33,100,145 ÷ 3 = 11,033,381.6667

If the quotient is a whole number, then 3 and 11,033,381.6667 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 33,100,145
-1 -33,100,145

Let's try dividing by 4:

33,100,145 ÷ 4 = 8,275,036.25

If the quotient is a whole number, then 4 and 8,275,036.25 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 33,100,145
-1 33,100,145
Keep dividing by the next highest number until you cannot divide anymore.

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

1513652411,2052,1133,13310,56515,66527,469137,345509,2332,546,1656,620,02933,100,145
-1-5-13-65-241-1,205-2,113-3,133-10,565-15,665-27,469-137,345-509,233-2,546,165-6,620,029-33,100,145

More Examples

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