Q: What are the factor combinations of the number 151,600,729?

 A:
Positive:   1 x 1516007297 x 2165724737 x 4097317259 x 585331683 x 221963857 x 1768974781 x 317095999 x 25271
Negative: -1 x -151600729-7 x -21657247-37 x -4097317-259 x -585331-683 x -221963-857 x -176897-4781 x -31709-5999 x -25271


How do I find the factor combinations of the number 151,600,729?

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 151,600,729, 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.

1 151,600,729
-1 -151,600,729

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 151,600,729.

Example:
1 x 151,600,729 = 151,600,729
and
-1 x -151,600,729 = 151,600,729
Notice both answers equal 151,600,729

With that explanation out of the way, let's continue. Next, we take the number 151,600,729 and divide it by 2:

151,600,729 ÷ 2 = 75,800,364.5

If the quotient is a whole number, then 2 and 75,800,364.5 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:

1 151,600,729
-1 -151,600,729

Now, we try dividing 151,600,729 by 3:

151,600,729 ÷ 3 = 50,533,576.3333

If the quotient is a whole number, then 3 and 50,533,576.3333 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:

1 151,600,729
-1 -151,600,729

Let's try dividing by 4:

151,600,729 ÷ 4 = 37,900,182.25

If the quotient is a whole number, then 4 and 37,900,182.25 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:

1 151,600,729
-1 151,600,729
Keep dividing by the next highest number until you cannot divide anymore.

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

17372596838574,7815,99925,27131,709176,897221,963585,3314,097,31721,657,247151,600,729
-1-7-37-259-683-857-4,781-5,999-25,271-31,709-176,897-221,963-585,331-4,097,317-21,657,247-151,600,729

More Examples

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