What is the HCF of 900 and 270?

The Highest Common Factor (HCF) of 900 and 270 is 90.

The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest number that divides two or more numbers without leaving a remainder. To find the HCF of 900 and 270, we can use several methods, such as prime factorization or the Euclidean algorithm.

Here's a breakdown:

1. Understanding HCF: The HCF is the greatest number that can perfectly divide both 900 and 270.

2. Methods to Calculate HCF:

   • Prime Factorization: Find the prime factors of each number and then identify the common factors.
   • Euclidean Algorithm: Repeatedly apply the division algorithm until the remainder is zero. The last non-zero remainder is the HCF.

3. Calculation:

   • Using the Euclidean Algorithm:
     • 900 = 270 * 3 + 90
     • 270 = 90 * 3 + 0

   Since the last non-zero remainder is 90, the HCF of 900 and 270 is 90.

Therefore, 90 is the largest number that can divide both 900 and 270 without leaving a remainder.