What is the HCF / GCF of 120, 180 and 190

in prime factorisation method

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To find the Highest Common Factor (HCF) or Greatest Common Factor (GCF) of a set of numbers using the prime factorization method, follow these steps:

1. Prime factorize each number:
- 120 = 2^3 * 3 * 5
- 180 = 2^2 * 3^2 * 5
- 190 = 2 * 5 * 19

2. Identify the common prime factors:
- The common prime factors among the three numbers are 2 and 5.

3. Determine the highest power of each common factor:
- The highest power of 2 is 2^2.
- The highest power of 5 is 1.

4. Multiply the common factors raised to their highest power:
- HCF/GCF = 2^2 * 5 = 20.

Therefore, the HCF or GCF of 120, 180, and 190 is 20.