66 as a product of prime factors
Understand the Problem
The question is asking for the prime factorization of the number 66, which involves breaking it down into its prime components. The solution will involve determining which prime numbers multiply together to equal 66.
Answer
$2 \times 3 \times 11$
Answer for screen readers
The prime factorization of 66 is $2 \times 3 \times 11$.
Steps to Solve
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Identify the smallest prime number Start with the smallest prime number, which is 2. Check if 66 is divisible by 2. Since 66 is even, divide 66 by 2: $$ 66 \div 2 = 33 $$
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Move to the next smallest prime Now we need to factor 33. The next smallest prime number is 3. Check if 33 is divisible by 3: $$ 33 \div 3 = 11 $$ 11 is prime, so we have reached the end of our factorization.
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Combine the prime factors Now we can write down the prime factorization of 66 using the factors we found: The prime factorization of 66 is: $$ 66 = 2 \times 3 \times 11 $$
The prime factorization of 66 is $2 \times 3 \times 11$.
More Information
Prime factorization is essential in many areas of mathematics, such as number theory and algebra. Factoring numbers helps in finding Least Common Multiples (LCM) and Greatest Common Divisors (GCD).
Tips
- Confusing composite numbers with prime numbers. Ensure that each factor is indeed a prime number.
- Forgetting to check each number systematically, which can result in missing some prime factors.
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