Question

Question 193

Fatima wants to mail three parcels to three village schools. She finds that the postal charges are ₹ 20, ₹ 28 and ₹ 36, respectively. If she wants to buy stamps only of one denomination, what is the greatest denomination of stamps she must buy to mail the three parcels?

Answer 1

Here, the greatest denomination of stamps that Fatima must buy to mail the three parcels, will be equal to the HCF of ₹ 20, ₹ 28 and₹ 36.

$\begin{array}{ccc}& 2& 20\\ & 2& 10\\ & 5& 5\\ & & 1\end{array}\begin{array}{ccc}& 2& 28\\ & 2& 14\\ & 7& 7\\ & & 1\end{array}\begin{array}{ccc}& 2& 36\\ & 2& 18\\ & 3& 9\\ & 3& 3\\ & & 1\end{array}$

Prime factorization of 20 $=2\times 2\times 5$

Prime factorization of 28 $=2\times 2\times 7$

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

Common factors of 20,28 and 36 are (occuring twice),

HCF of 20, 28 and 36 $=2\times 2=4$

Thus, the greatest denomination of stamps that Fatima must buy, is ₹ 4.