Question

Four drums containing water have capacities 135 litres, 205 litres, 165 litres and 240 litres. Find the greatest capacity measure which can be used to measure the capacities of the drum. *

Answer 1

We are given four drums of capacities :

$c_{1}$ = 135 litres  

$c_{2}$ = 205 litres

$c_{3}$ = 165 litres

$c_{4}$= 240 litres

We have to find the greatest capacity of a measure which can measure all of them  

i.e. we have to find a number which is highest and common to 135, 205, 165 and 240.

We need to find Highest Common Multiple(HCF) of the 4 numbers.

Using factorization method:

$135 = \underline{5} \times 3 \times 3 \times 3\\205 = \underline{5} \times 41\\165 = \underline{5} \times 3 \times 11\\240 = \underline{5} \times 3 \times 2 \times 2 \times 2 \times 2$

Common factor in all the four number is underlined as shown above.

HCF is 5.

Hence, 5 is the greatest capacity that can measure all the four capacities.