Question

Three mugs contains 1401 mL, 1434 mL and 1464 mL of water respectively. Find the maximum capacity of the mug that can exactly measure the water of the three mugs?

• A. 5 mL
• B. 3 mL
  
• C. 1 mL
  
• D. 7 mL
  

Answer 1

The correct option is B 3 mL


The capacity of three given mugs are: 1401 mL, 1434 mL, 1464 mL.

The maximum capacity of the mug that can exaclty measure the water of all the three mugs will be the greatest number that is able to divide the quantity of all the three mugs completely.

So, to get that capacity, we need to find the HCF of 1401, 1434 and 1464.

We will find HCF through prime factorisation;

$\begin{array}{cc}3& 1401\\ 467& 467\\ & 1\end{array}$

$\begin{array}{cc}2& 1434\\ 3& 717\\ 239& 239\\ & 1\end{array}$

$\begin{array}{cc}2& 1464\\ 2& 732\\ 2& 366\\ 3& 183\\ 61& 61\\ & 1\end{array}$

1401 = 3 $\times$ 467
1434 = 2 $\times$ 3 $\times$ 239
1464 = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 61

HCF of (1401, 1434, 1464) = 3.

Hence, the maximum capacity of the mug that can exactly measure the water of all the three given mugs is 3 mL.