Highest Common Factor (HCF) / Greatest Common Divisor (GCD) : Solved Examples

Elucid's Division Lemma Method

Prime Factorisation Method

Successive Division Method

Two tanks of capacity 105 and 175 liters is to be filled with water. Find maximum capacity of third tank which can fill both the tanks completely and also find in how many refills will third tank fill both the tanks. Given in the question: Tank 1 capacity = 105 liters Tank 2 capacity = 165 liters Now, as per the question, the solution will be two parts: Part 1 = Find maximum capacity of third tank which can fill both the tanks completely So, we find maximum capacity of third tank, take HCF of capacity of both tanks and we get: HCF of 105 & 165 = 35 Therefore, maximum capacity of third which will fill both the tank completely = 35 liters Part 2 = Find in how many refills will third tank fill both the tanks. To calculate number of refills required by third to find both tank, divide capacity of tank 1 and tank 2 by capacity of third tank and we get: Refills for tank 1 = 105 ÷ 35 = 3 refills Refills for tank 2 = 175 ÷ 35 = 5 refills Related Question Examples Two tanks of capacity 105 and 175 liters is to be filled with water. Find maximum capacity of third tank which can fill both the tanks completely and also find in how many refills will third tank fill both the tanks. Robert purchased three bags of sand weighing 80 kg, 85 kg & 90 kg respectively. Now he wants to check the weight of all these bags. Find the maximum weight he should choose so that each bag weight can be checked completely. Dimensions a hall is 91 m, 112 m and 49 m. Find the length of longest tape which can measure all the dimensions of the room exactly.