Question

Find the greatest number that will divide 79,117 and 59 leaving the remainder 7,9, and 11 respectively.

Answer 1

From 79 we want remainder 7 so to make it perfectly divisible we need to subtract 7.

:. 79 - 7 = 72 ---------------------- 1

From 117 we want remainder 9 so to make it perfectly divisible we need to subtract 9.

:. 117 - 9 = 108 -------------------- 2

From 59 we want remainder 11 so to make it perfectly divisible we need to subtract 11 .

:. 59 - 11 = 48 ---------------------- 3




Now for greatest number

We need to find the HCF of 72 , 108 , 48 .

72 = 2 × 2 × 2 × 3 × 3

108 = 2 × 2 × 3 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3


Therefore HCF = 2 × 2 × 3

= 12


So the greatest number by which 79 , 117 and 59 will leave remainder 7 , 9 , 11 respectively is 12 .