# What is the prime factorization of 55?

#### Understand the Problem

The question is asking for the prime factorization of the number 55, which means we need to break 55 down into its prime factors.

The prime factorization of 55 is $5 \times 11$.

The prime factorization of 55 is $5 \times 11$.

#### Steps to Solve

1. Identify the smallest prime number Start by identifying the smallest prime number, which is 2. Check if 55 is divisible by 2.

2. Check divisibility by 2 Since 55 is an odd number, it is not divisible by 2. Move to the next smallest prime number, which is 3.

3. Check divisibility by 3 Divide 55 by 3. The result is not an integer (approximately 18.33), so 55 is not divisible by 3. Proceed to the next prime number, which is 5.

4. Check divisibility by 5 Now check if 55 is divisible by 5. Since 55 ends in 5, it is divisible by 5. We calculate: $$55 \div 5 = 11$$

5. Check if the quotient is prime The quotient we obtained is 11. We need to check if 11 is a prime number. A prime number has only two divisors: 1 and itself. The only divisors of 11 are 1 and 11, confirming that it is prime.

6. Write the prime factorization Finally, express the prime factorization of 55 using its prime factors: $$55 = 5 \times 11$$

The prime factorization of 55 is $5 \times 11$.