To find the HCF (Highest Common Factor) of two or more numbers, please follow these steps:
- List the prime factors of each number.
- Identify the common prime factors.
- Multiply those common prime factors.
For example, let’s find the HCF of 24 and 36.
Step 1: Prime factorization of 24 = 2 x 2 x 2 x 3 Prime factorization of 36 = 2 x 2 x 3 x 3
Step 2: The common prime factors are 2 and 3.
Step 3: Multiply the common prime factors: 2 x 2 x 3 = 12
Therefore, the HCF of 24 and 36 is 12.
You can use a calculator to find the prime factorization or manually find the prime factors.
HCF stands for “highest common factor”, which is the largest positive integer that divides two or more numbers without leaving a remainder. For example, the HCF of 12 and 18 is 6, because 6 is the largest number that can divide both 12 and 18 without leaving a remainder.
To find the HCF of two or more numbers, you can use various methods such as prime factorization, Euclid’s algorithm, or listing out the factors and finding the common ones. The method you use may depend on the size and nature of the numbers.
Here is an example of finding the HCF of two numbers using prime factorization:
- Write the prime factorization of each number.
- 36 = 2^2 × 3^2
- 48 = 2^4 × 3
- Identify the common prime factors and their lowest exponent.
- The common prime factors are 2 and 3.
- The lowest exponent of 2 is 2, and the lowest exponent of 3 is 1.
- Multiply the common prime factors with their lowest exponent.
- HCF = 2^2 × 3^1 = 12
Therefore, the HCF of 36 and 48 is 12.