Question

find the largest number which divides 69 and 124 leaving remainders 4 and 7 respectively​

Answer 1

Answer:

13

Step-by-step explanation:

Given numbers are 69 and 124 and remainders are 4 and 7 respectively. Then new numbers after subtracting remainders are :

69 – 4 = 65

124 – 7 = 117

The required number is HCF of 65 and 117.

HCF by prime factorization method :

Prime factorization of 65 = 5 × 13

Prime factorization of 117 = 3×3×13= = 3²×13

HCF of 65 and 117 = 13  

[HCF of two or more numbers =  product of the smallest power of each common prime factor involved in the numbers.]

HCF of 69 and 117 is 13.

Hence, the required greatest number which divides 69 and 124 leaving remainders 4 and 7 respectively is 13.

HOPE THIS WILL HELP YOU….