What is the prime factorization of 68?
Understand the Problem
The question is asking for the prime factorization of the number 68. Prime factorization involves breaking down the number into its prime number factors, which are the smallest prime numbers that multiply together to give the original number.
Answer
The prime factorization of 68 is $2^2 \times 17$.
Answer for screen readers
The prime factorization of 68 is $2^2 \times 17$.
Steps to Solve
- Start with the original number
Begin with the number 68.
- Divide by the smallest prime number
The smallest prime number is 2. Check if 68 is divisible by 2: $$ 68 \div 2 = 34 $$ So, 2 is one of the prime factors. We can continue factoring 34.
- Factor the next number
Now, take 34 and divide by 2 again: $$ 34 \div 2 = 17 $$ Thus, we have another prime factor, which is also 2.
- Check if the last number is prime
Next, we have the number 17. Check if it is a prime number. A prime number is only divisible by 1 and itself. Since 17 cannot be divided by any prime number other than 1 and 17, it is a prime number.
- Combine all prime factors
Now we can write the prime factorization of 68: The prime factorization can be expressed as: $$ 68 = 2^2 \times 17 $$
The prime factorization of 68 is $2^2 \times 17$.
More Information
The prime factorization helps in number theory, particularly in finding least common multiples or greatest common divisors. It can also be used in simplifying fractions.
Tips
- Not dividing by the smallest prime: Sometimes, people might attempt to divide by other numbers without checking if 2 or other smaller primes can divide first.
- Ignoring prime status: Forgetting to check if the last number after factorization is a prime can lead to incorrect results.
