What is the HCF of 24 and 36?

To find the highest common factor (HCF) of 24 and 36, we can use a few different methods, such as prime factorization, listing factors, or the Euclidean algorithm. Here’s one possible method using prime factorization:

Step 1: Prime factorize each number.

• 24 = 2 × 2 × 2 × 3
• 36 = 2 × 2 × 3 × 3

Step 2: Identify the common prime factors and their minimum exponents.

• The common prime factors are 2 and 3.
• The minimum exponent of 2 is 2 (i.e., it appears twice in both factorizations).
• The minimum exponent of 3 is 1 (i.e., it appears once in both factorizations).

Step 3: Multiply the common prime factors with their minimum exponents.

• HCF(24, 36) = 2² × 3¹
• HCF(24, 36) = 12

Therefore, the HCF of 24 and 36 is 12.