What is the prime factorization of 82?
Understand the Problem
The question is asking for the prime factors of the number 82, which means we need to find the prime numbers that multiply together to give 82.
Answer
The prime factors of 82 are $2$ and $41$.
Answer for screen readers
The prime factors of 82 are $2$ and $41$.
Steps to Solve
- Find the smallest prime factor of 82
Start by checking the smallest prime number, which is 2.
Since 82 is an even number, it is divisible by 2.
Calculate: $$ 82 \div 2 = 41 $$
- Check if the quotient (41) is a prime number
Now we need to check if 41 is a prime number. A prime number is only divisible by 1 and itself.
Check divisibility by prime numbers less than the square root of 41. The primes are 2, 3, 5.
- 41 is not even, so not divisible by 2.
- For 3: $4 + 1 = 5$, which is not divisible by 3.
- For 5: 41 does not end in 0 or 5, so it is not divisible by 5.
Since it is not divisible by any of these primes, 41 is a prime number.
- List the prime factors
Combining the factors found: The prime factors of 82 are $2$ and $41$.
The prime factors of 82 are $2$ and $41$.
More Information
Prime factorization is a way of expressing a number as a product of prime numbers. Every integer greater than 1 can be factored uniquely into prime numbers, known as its prime factorization.
Tips
- Forgetting to check if the quotient is prime: After dividing by a prime, it's important to check if the result is also a prime.
- Not checking all possible primes: Make sure to check divisibility against all relevant prime numbers.
AI-generated content may contain errors. Please verify critical information
