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.
Answer
The prime factorization of 55 is $5 \times 11$.
Answer for screen readers
The prime factorization of 55 is $5 \times 11$.
Steps to Solve
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Identify the smallest prime number Start by identifying the smallest prime number, which is 2. Check if 55 is divisible by 2.
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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.
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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.
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Check divisibility by 5 Now check if 55 is divisible by 5. Since 55 ends in 5, it is divisible by 5. We calculate: $$ 55 \div 5 = 11 $$
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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.
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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 $5 \times 11$.
More Information
The number 55 is a product of two prime numbers, 5 and 11. This means that 55 can only be divided evenly by those two numbers along with 1. Understanding prime factorization is crucial in number theory, as it helps in simplifying fractions, finding least common multiples, and determining greatest common divisors.
Tips
- Forgetting to test all prime numbers up to the square root of 55 may lead to missing a prime factor.
- Incorrectly assuming that all even numbers are primes (like confusing 2 with higher even numbers).
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