Q: What are the factor combinations of the number 150,145,307?

 A:
Positive:   1 x 15014530713 x 1154963931 x 484339747 x 3194581403 x 372569611 x 2457371457 x 1030517927 x 18941
Negative: -1 x -150145307-13 x -11549639-31 x -4843397-47 x -3194581-403 x -372569-611 x -245737-1457 x -103051-7927 x -18941


How do I find the factor combinations of the number 150,145,307?

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 150,145,307, 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.

1 150,145,307
-1 -150,145,307

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 150,145,307.

Example:
1 x 150,145,307 = 150,145,307
and
-1 x -150,145,307 = 150,145,307
Notice both answers equal 150,145,307

With that explanation out of the way, let's continue. Next, we take the number 150,145,307 and divide it by 2:

150,145,307 ÷ 2 = 75,072,653.5

If the quotient is a whole number, then 2 and 75,072,653.5 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:

1 150,145,307
-1 -150,145,307

Now, we try dividing 150,145,307 by 3:

150,145,307 ÷ 3 = 50,048,435.6667

If the quotient is a whole number, then 3 and 50,048,435.6667 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:

1 150,145,307
-1 -150,145,307

Let's try dividing by 4:

150,145,307 ÷ 4 = 37,536,326.75

If the quotient is a whole number, then 4 and 37,536,326.75 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:

1 150,145,307
-1 150,145,307
Keep dividing by the next highest number until you cannot divide anymore.

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

11331474036111,4577,92718,941103,051245,737372,5693,194,5814,843,39711,549,639150,145,307
-1-13-31-47-403-611-1,457-7,927-18,941-103,051-245,737-372,569-3,194,581-4,843,397-11,549,639-150,145,307

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