Find the HCF of the numbers 18 and 24.
Understand the Problem
The question focuses on understanding mathematical concepts related to LCM (Least Common Multiple) and HCF (Highest Common Factor) of numbers. It likely involves how to find the HCF of two or more numbers using the prime factorization method.
Answer
The HCF of 18 and 24 is $6$.
Answer for screen readers
The HCF of the numbers 18 and 24 is $6$.
Steps to Solve
-
Identify the numbers We need to find the HCF of the numbers given, which are 18 and 24.
-
Prime factorization of both numbers Find the prime factors for each number:
-
For 18:
- 18 can be factored into $2 \times 9$, and $9$ can be further factored into $3 \times 3$.
- So, the prime factorization of 18 is $2^1 \times 3^2$.
-
For 24:
- 24 can be factored into $2 \times 12$, and $12$ can be further factored into $3 \times 4$, and $4$ into $2 \times 2$.
- So, the prime factorization of 24 is $2^3 \times 3^1$.
- Identify common prime factors From the prime factorizations:
- 18: $2^1 \times 3^2$
- 24: $2^3 \times 3^1$
The common prime factors are:
- The lowest power of 2 is $2^1$.
- The lowest power of 3 is $3^1$.
- Multiply the common factors To find the HCF, multiply the common prime factors: $$ \text{HCF} = 2^1 \times 3^1 = 2 \times 3 = 6 $$
The HCF of the numbers 18 and 24 is $6$.
More Information
The Highest Common Factor (HCF), also known as Greatest Common Divisor (GCD), is used to find the largest number that divides two or more numbers without leaving a remainder. It is useful in simplifying fractions, finding common denominators, and solving problems involving ratios.
Tips
- Forgetting to include all common prime factors: Ensure all prime factors are considered when looking for the HCF.
- Multiplying incorrectly: Double-check multiplication of common factors to avoid errors in the final HCF.
AI-generated content may contain errors. Please verify critical information
