What is the prime factor of 68?
Understand the Problem
The question is asking for the prime factors of the number 68. To solve this, we need to find the prime numbers that, when multiplied together, give the product of 68.
Answer
The prime factors of 68 are $2$ and $17$.
Answer for screen readers
The prime factors of 68 are $2$ and $17$.
Steps to Solve
- Divide by the smallest prime number
Start with the smallest prime number, which is 2. Check if 68 is divisible by 2.
$$ 68 \div 2 = 34 $$
Since the result is a whole number, 2 is a prime factor of 68.
- Continue factoring
Next, take the quotient obtained and check if it's divisible by 2 again.
$$ 34 \div 2 = 17 $$
So, 2 is also a prime factor again.
- Check if the remaining number is prime
Now, we have 17, which we need to check if it is a prime number. The only divisors of 17 are 1 and 17 itself, indicating that it is a prime number.
- List all prime factors
At this point, we have ( 68 = 2 \times 2 \times 17 ). The prime factors can be represented as:
$$ 2^2 \times 17 $$
Thus, the prime factors of 68 are 2 and 17.
The prime factors of 68 are $2$ and $17$.
More Information
The prime factorization process helps in understanding how numbers can be broken down into their building blocks. The number 68 is unique in that it is even and its factors include both a square of a prime and another distinct prime.
Tips
- Not checking if the remaining quotient is prime.
- Skipping the step of dividing by the smallest prime, which can lead to incorrect factors.