Q: What are the factor combinations of the number 150,634,501?

 A:
Positive:   1 x 15063450117 x 886085397 x 1552933167 x 902003547 x 2753831649 x 913492839 x 530599299 x 16199
Negative: -1 x -150634501-17 x -8860853-97 x -1552933-167 x -902003-547 x -275383-1649 x -91349-2839 x -53059-9299 x -16199


How do I find the factor combinations of the number 150,634,501?

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 150,634,501, 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.

1 150,634,501
-1 -150,634,501

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 150,634,501.

Example:
1 x 150,634,501 = 150,634,501
and
-1 x -150,634,501 = 150,634,501
Notice both answers equal 150,634,501

With that explanation out of the way, let's continue. Next, we take the number 150,634,501 and divide it by 2:

150,634,501 ÷ 2 = 75,317,250.5

If the quotient is a whole number, then 2 and 75,317,250.5 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:

1 150,634,501
-1 -150,634,501

Now, we try dividing 150,634,501 by 3:

150,634,501 ÷ 3 = 50,211,500.3333

If the quotient is a whole number, then 3 and 50,211,500.3333 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:

1 150,634,501
-1 -150,634,501

Let's try dividing by 4:

150,634,501 ÷ 4 = 37,658,625.25

If the quotient is a whole number, then 4 and 37,658,625.25 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:

1 150,634,501
-1 150,634,501
Keep dividing by the next highest number until you cannot divide anymore.

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

117971675471,6492,8399,29916,19953,05991,349275,383902,0031,552,9338,860,853150,634,501
-1-17-97-167-547-1,649-2,839-9,299-16,199-53,059-91,349-275,383-902,003-1,552,933-8,860,853-150,634,501

More Examples

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