Q: What are the factor combinations of the number 150,306,929?

 A:
Positive:   1 x 15030692919 x 791089167 x 224338771 x 21169991273 x 1180731349 x 1114211663 x 903834757 x 31597
Negative: -1 x -150306929-19 x -7910891-67 x -2243387-71 x -2116999-1273 x -118073-1349 x -111421-1663 x -90383-4757 x -31597


How do I find the factor combinations of the number 150,306,929?

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 150,306,929, 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.

1 150,306,929
-1 -150,306,929

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 150,306,929.

Example:
1 x 150,306,929 = 150,306,929
and
-1 x -150,306,929 = 150,306,929
Notice both answers equal 150,306,929

With that explanation out of the way, let's continue. Next, we take the number 150,306,929 and divide it by 2:

150,306,929 ÷ 2 = 75,153,464.5

If the quotient is a whole number, then 2 and 75,153,464.5 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:

1 150,306,929
-1 -150,306,929

Now, we try dividing 150,306,929 by 3:

150,306,929 ÷ 3 = 50,102,309.6667

If the quotient is a whole number, then 3 and 50,102,309.6667 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:

1 150,306,929
-1 -150,306,929

Let's try dividing by 4:

150,306,929 ÷ 4 = 37,576,732.25

If the quotient is a whole number, then 4 and 37,576,732.25 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:

1 150,306,929
-1 150,306,929
Keep dividing by the next highest number until you cannot divide anymore.

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

11967711,2731,3491,6634,75731,59790,383111,421118,0732,116,9992,243,3877,910,891150,306,929
-1-19-67-71-1,273-1,349-1,663-4,757-31,597-90,383-111,421-118,073-2,116,999-2,243,387-7,910,891-150,306,929

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