Three different containers contain different quantities of mixtures of milk and water, whose measurements are 403 kg, 434 kg and 465 kg What biggest measure can measure all the different quantities exactly?

Given :

The given measurements of container are 403 kg ,434 kg and 465 kg.

To find :

We have to find the biggest measure that can measure the given quantities exactly. 

Solution :

Highest common factor of 403 , 434 and 465 is the biggest measure that can measure the given quantities exactly.

Prime factorization of 403 $= 13 \times 31$

Prime factorization of 434 $= 2\times 7 \times 31$

Prime factorization of 465 $= 3 \times 5 \times 31$

HCF $=$  Smallest power of the common factor.

So, HCF of 403 , 434 and 465 $=$ 31.

Therefore, the biggest measure that can measure the given quantities exactly is 31 kg.

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Updated on: 10-Oct-2022

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