Answer :
The prime decomposition of 819 is 3 × 3 × 7 × 13. This means that in the prime factorization of 819, there are two 3's, one 7, and one 13, while there are zero 2's, 5's, and 11's.
To find the prime decomposition of 819, we need to divide it by the smallest primes until we get a quotient of 1. Let's begin the process:
- 81 is divisible by 3 (since 8 + 1 + 9 = 18, which is divisible by 3), so we get 819 ÷ 3 = 273.
- 273 is also divisible by 3, so we get 273 ÷ 3 = 91.
- 91 is not divisible by 3 but is divisible by 7, so we get 91 ÷ 7 = 13.
- 13 is a prime number, so we have completed the prime factorization.
- The prime decomposition of 819 is 3 × 3 × 7 × 13.
Now answering the rest of the question:
There are zero 2's since 819 is not divisible by 2.
- There are two 3's.
- There are zero 5's.
- There is one 7.
- There are zero 11's.
- There is one 13.
