150 as a product of primes use index rotation where appropiate
Answers
Start with the smallest possible prime number (i.e., 2), keep dividing your number by it until it does no longer divide. Write down the power of 2 by which you divided (could be 2020 , if you started with an odd number).
Repeat this for the newly obtained quotient, but now dividing by the next smallest prime number (i.e., 3). Again, write down the power of 3, and continue with what’s left.
Keep doing this until you end up with the number 1 (which you ignore).
The prime factor decomposition is the product of all prime powers you wrote down (but don’t write down the cases with power 0).
For the number 150, that would give:
2121 , and you’re left with 75
3131 , and you’re left with 25
5252 , and you’re left with 1, so there it stops.
Putting it together, the prime factor decomposition of 150 is 21⋅31⋅5221⋅31⋅52 , or just 2⋅3⋅522⋅3⋅52 , or even just 2⋅3⋅5⋅52⋅3⋅5⋅5 , if you don’t like exponents.