Find the HCF using the prime factorization method the number is 120 and 261

Answer: 3

Step-by-step solution

Step 1: Prime Factorisation of 120

We first express 120 as a product of its prime factors. Dividing successively by prime numbers gives $120 = 2 \times 60 = 2^2 \times 30 = 2^3 \times 15 = 2^3 \times 3 \times 5$ .

Step 2: Prime Factorisation of 261

Next, we find the prime factors of 261. The sum of digits is $2 + 6 + 1 = 9$ , which is divisible by 9, giving $261 = 3 \times 87 = 3^2 \times 29$ , where 29 is a prime number.

Step 3: Identify Common Prime Factors and Find HCF

The HCF is the product of the smallest powers of each common prime factor. The only common prime factor between $120$ and $261$ is $3$ , and the smallest power is $3^1$ . Therefore, $\text{HCF}(120, 261) = 3$ .

Solve your own maths question free →