Final answer:
To express 33 as a product of its prime factors, divide by the smallest prime number until you reach a prime number. The prime factorization of 33 is 3 × 11. To express 66 as a product of its prime factors, divide by the smallest prime number until you reach a prime number. The prime factorization of 66 is 2 × 3 × 11. The greatest common factor of 33 and 66 is 33. 33 can be rewritten as 33 × 1 and 66 can be rewritten as 33 × 2 using their GCF and multiplication.
Step-by-step explanation:
To express 33 as a product of its prime factors, we need to find the prime numbers that multiply together to give 33. One way to do this is to divide 33 by the smallest prime number, which is 3. We get 33 ÷ 3 = 11. Since 11 is a prime number, we stop here. Therefore, 33 = 3 × 11.
To express 66 as a product of its prime factors, we divide 66 by 2 since 2 is the smallest prime number that divides evenly into 66. We get 66 ÷ 2 = 33. Now we can use the prime factorization of 33 that we found earlier, which is 3 × 11. Therefore, 66 = 2 × 3 × 11.
The greatest common factor (GCF) of 33 and 66 can be found by finding the common factors and selecting the greatest one. The factors of 33 are 1, 3, 11, and 33. The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. The greatest common factor of 33 and 66 is 33.
To rewrite 33 and 66 using their GCF and multiplication, we can divide both numbers by the GCF. 33 ÷ 33 = 1 and 66 ÷ 33 = 2. So, 33 = 33 × 1 and 66 = 33 × 2.