Next, we express 867 and 255 as products of their prime factors. Since 867 = 3 × 289 and 289 = 17², we have 867 = 3 × 17². For 255, dividing by 3 and 5 gives 3 × 5 × 17.

HCF of 72 and 120 find the HCF 867 and 255

Answer: $\text{HCF}(72, 120) = 24$ and $\text{HCF}(867, 255) = 51$

Step-by-step solution

Step 1: Prime factorisation of 72 and 120

We express both $72$ and $120$ as products of their prime factors in exponent form. For $72$ , dividing repeatedly by prime factors gives $2^3 \times 3^2$ . For $120$ , dividing gives $2^3 \times 3 \times 5$ .

Step 2: Find the HCF of 72 and 120

The HCF is the product of the smallest power of each common prime factor involved in the numbers. The common prime factors are $2$ and $3$ , with smallest powers $2^3$ and $3^1$ respectively, giving an HCF of $24$ .

Step 3: Prime factorisation of 867 and 255

Next, we express $867$ and $255$ as products of their prime factors. Since $867 = 3 \times 289$ and $289 = 17^2$ , we have $867 = 3 \times 17^2$ . For $255$ , dividing by $3$ and $5$ gives $3 \times 5 \times 17$ .

Step 4: Find the HCF of 867 and 255

The common prime factors are $3$ and $17$ . The smallest power of $3$ is $3^1$ and the smallest power of $17$ is $17^1$ . Multiplying these gives $\text{HCF}(867, 255) = 51$ .

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