Question

What is the remainder when x = (29 × 37 × 42 × 65 × 73 × 57) is divided by 45?
1. 5
2. 0
3. 3
4. 1

Answer 1

Correct Answer - Option 2 : 0

Given:

x = (29 × 37 × 42 × 65 × 73 × 57)/45

Calculations:

x = (29 × 37 × 42 × 65 × 73 × 57)/(3² × 5)

⇒ x = (29 × 37 × (3 × 16) × (5 × 13) × 73 × (3 × 19))/(32 × 5)

We observe x is multiple of 3² and 5 both

⇒ x is divisible by 45

⇒ Remainder = 0

∴ The remainder when x is divided by 45 is 0.