What is the Highest Common Factor of 125 and 225?

The Highest Common Factor (HCF) of 125 and 225 is 25.

Understanding Highest Common Factor (HCF)

The Highest Common Factor, also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more integers without any remainder.

Calculating HCF of 125 and 225

We can find the HCF of 125 and 225 using various methods. Here, we'll show two common methods: listing factors and prime factorization.

Method 1: Listing Factors

1. List the factors of each number:

   • Factors of 125: 1, 5, 25, 125
   • Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225

2. Identify the common factors: 1, 5, 25

3. Determine the highest common factor: The highest common factor is 25.

Method 2: Prime Factorization

1. Find the prime factorization of each number:

   • 125 = 5 x 5 x 5 = 5³
   • 225 = 3 x 3 x 5 x 5 = 3² x 5²

2. Identify the common prime factors and their lowest powers: The common prime factor is 5, and its lowest power is 5².

3. Multiply the common prime factors with their lowest powers: 5² = 25

Therefore, the HCF of 125 and 225 is 25.

Reference Confirmation

According to the provided reference: HCF of (125,225) = 25.