Q: What are the factor combinations of the number 154,303,009?

 A:
Positive:   1 x 1543030097 x 2204328719 x 812121149 x 3149041133 x 1160173343 x 449863931 x 1657396517 x 23677
Negative: -1 x -154303009-7 x -22043287-19 x -8121211-49 x -3149041-133 x -1160173-343 x -449863-931 x -165739-6517 x -23677


How do I find the factor combinations of the number 154,303,009?

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 154,303,009, 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.

1 154,303,009
-1 -154,303,009

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 154,303,009.

Example:
1 x 154,303,009 = 154,303,009
and
-1 x -154,303,009 = 154,303,009
Notice both answers equal 154,303,009

With that explanation out of the way, let's continue. Next, we take the number 154,303,009 and divide it by 2:

154,303,009 ÷ 2 = 77,151,504.5

If the quotient is a whole number, then 2 and 77,151,504.5 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:

1 154,303,009
-1 -154,303,009

Now, we try dividing 154,303,009 by 3:

154,303,009 ÷ 3 = 51,434,336.3333

If the quotient is a whole number, then 3 and 51,434,336.3333 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:

1 154,303,009
-1 -154,303,009

Let's try dividing by 4:

154,303,009 ÷ 4 = 38,575,752.25

If the quotient is a whole number, then 4 and 38,575,752.25 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:

1 154,303,009
-1 154,303,009
Keep dividing by the next highest number until you cannot divide anymore.

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

1719491333439316,51723,677165,739449,8631,160,1733,149,0418,121,21122,043,287154,303,009
-1-7-19-49-133-343-931-6,517-23,677-165,739-449,863-1,160,173-3,149,041-8,121,211-22,043,287-154,303,009

More Examples

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