Write 66 as a product of prime factors.
Understand the Problem
The question is asking for the prime factorization of the number 66. This involves expressing 66 as a product of its prime factors. To solve it, we will divide 66 by the smallest prime numbers until we reach 1.
Answer
The prime factorization of 66 is \( 2 \times 3 \times 11 \).
Answer for screen readers
The prime factorization of 66 is ( 2 \times 3 \times 11 ).
Steps to Solve
- Start with the number 66
We begin with the number 66, and we need to find the smallest prime number that divides it.
- Divide by the smallest prime number
The smallest prime number is 2.
Now, we can divide 66 by 2:
$$ 66 \div 2 = 33 $$
So, we have found that:
$$ 66 = 2 \times 33 $$
- Continue factoring 33
Next, we need to factor 33. Again, we start with the smallest prime numbers. Since 33 is odd, we cannot divide it by 2.
The next smallest prime number is 3:
$$ 33 \div 3 = 11 $$
Now we can express 33 as:
$$ 33 = 3 \times 11 $$
Putting it all together, we have:
$$ 66 = 2 \times 3 \times 11 $$
- Confirm that 11 is prime
Finally, we need to check if 11 is a prime number. Since its only divisors are 1 and 11, it is confirmed that 11 is prime.
Thus, the complete 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 important in number theory and helps in simplifying fractions, finding least common multiples, and greatest common divisors.
Tips
- Forgetting to check if the factors found are prime. Always ensure each factor is prime before concluding the factorization.
- Stopping the factorization process too early; make sure to divide until reaching all prime factors.
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