Three containers contain 27 litres, 36 litres and 72 litres of milk. What biggest measure can measure exactly the milk in the three containers?

Given :

The given containers contain 27 litres, 36 litres and 72 litres of milk.

To find :

We have to find the biggest measure which can measure exactly the milk in the three containers.

Solution :

The highest common factor of 27, 36, 72 is the biggest measure we required.

Prime factorization of $27 = 3 \times 3 \times 3 = 3^3$

Prime factorization of $36 = 2 \times 2 \times 3 \times 3= 2^2 \times 3^2$

Prime factorization of $72 = 2 \times 2 \times 2 \times 3 \times 3= 2^3 \times 3^2$

HCF $=$ Smallest power of the common factor.

HCF $= 3^2 = 9$

Therefore, 9 litre is the biggest measure which can measure exactly the milk in the three containers.

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Updated on: 10-Oct-2022

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