What is the prime factorization of 83?
Understand the Problem
The question is asking for the prime factorization of the number 83. Since 83 is a prime number itself, it does not have any other prime factors apart from 1 and 83. Thus, its prime factorization will simply be expressed as 83.
Answer
The prime factorization of 83 is $83$.
Answer for screen readers
The prime factorization of 83 is $83$.
Steps to Solve
- Determine if the number is prime
Check if 83 is divisible by any prime numbers up to its square root. The square root of 83 is approximately 9.11. The prime numbers less than or equal to 9 are 2, 3, 5, and 7.
- Check divisibility by 2
Since 83 is odd, it is not divisible by 2.
- Check divisibility by 3
Add the digits of 83: $8 + 3 = 11$. Since 11 is not divisible by 3, 83 is not divisible by 3.
- Check divisibility by 5
Since 83 does not end in 0 or 5, it is not divisible by 5.
- Check divisibility by 7
Calculate $83 \div 7 \approx 11.86$. Since this is not an integer, 83 is not divisible by 7.
- Conclude the factorization
Since 83 is not divisible by any prime number less than or equal to 9, it is confirmed that 83 is a prime number. Therefore, its prime factorization is simply 83.
The prime factorization of 83 is $83$.
More Information
Since 83 is a prime number, it only has two positive divisors: 1 and itself. Prime numbers play a crucial role in number theory and are the building blocks for all integers.
Tips
- Confusing prime factors with all factors: Remember that a prime number only has two factors, 1 and itself.
