Question

Using prime factorisation, find the HCF of 180, 140 and 210.

Hint:

List the prime factors of each number and take the product of the lowest powers of common factors.

Answer 1

Problem: Find the Highest Common Factor (HCF) of 180, 140, and 210 using prime factorization. Solution: 1. Prime Factorization: \[ 180 = 2^2 \times 3^2 \times 5 \] \[ 140 = 2^2 \times 5 \times 7 \] \[ 210 = 2 \times 3 \times 5 \times 7 \] 2. Identify Common Factors (Lowest Powers): * 2: \(2^1\) (from 210) * 3: Excluded (140 has no 3) * 5: \(5^1\) * 7: Excluded (180 has no 7) 3. Calculate HCF: \[ \text{HCF} = 2^1 \times 5^1 = 2 \times 5 = 10 \] Answer: \[ \boxed{10} \]