Question

When 61 and  74 are divided by a number we got 5 and 4 respectively as remainder, find highest such number. 
1. 7
2. 14
3. 21
4. 28

Answer 1

Correct Answer - Option 2 : 14

Concept used :

HCF is the highest common number that divides all the number of a set. 

Calculations :

Number divisible = 56 and 70             (first number = (61 - 5) and second number = 74 - 4)

HCF of 56 and 70 

56 = 8 × 7 = 2³ × 7

70 = 7 × 2 × 5

HCF of 56 and 70 = 7 × 2         (7 × 2 is the factor of both 56 and 70)

⇒ 14 

∴ Option 2 will be the correct choice.