1. **State the problem:** Find the highest common factor (HCF) of 156 and 260. 2. **Formula and method:** The HCF of two numbers is the largest number that divides both without leaving a remainder. We use the Euclidean algorithm: $$\text{HCF}(a,b) = \text{HCF}(b, a \bmod b)$$ 3. **Apply Euclidean algorithm:** $$260 \div 156 = 1 \text{ remainder } 104$$ So, $$\text{HCF}(156, 260) = \text{HCF}(156, 104)$$ 4. Next step: $$156 \div 104 = 1 \text{ remainder } 52$$ So, $$\text{HCF}(156, 104) = \text{HCF}(104, 52)$$ 5. Next step: $$104 \div 52 = 2 \text{ remainder } 0$$ Since remainder is 0, the HCF is 52. 6. **Final answer:** $$\boxed{52}$$