Question

Aroon had 49 paintings of one artist and 35 of another. He wanted to cover each wall with the same number of paintings. What is the minimum number of walls he can cover?

Answer 1

Aroon wants to cover each wall with the same number of paintings.
⇒ The number of paintings put up must be a common factor of 49 and 35.

Since the question is asking for the maximum number of paintings a wall can have, we are looking at the largest common factor of 49 and 35 = HCF(49 , 35)

Factors of 49 = 1, 7, 49
Factors of 35 = 1, 5, 7, 35
Common factors = 1, 7
HCF = 7

Thus, the maximum number of paintings a wall can have is 7.

The number of walls will be minimum if each wall has the maximum number of paintings.
⇒ Minimum number of walls = (49 +35) / HCF(49, 35)
= 49/7 + 35/7 = 12