Question

Find the largest number which gives out reminders 2 and 5 when used




to divide 80 and 122 b

Answer 1

Find the greatest number that will divide 55, 127 and 175 so as to leave the same remainder in each case. The required number would be the greatest number that divides 127-55 and 175 - 125, ie 72 and 48. The HCF of 72 and 48 is 24.

Answer 2

CONCEPT:

The concept of highest common factor(HCF)is used here.

HIGHEST COMMON FACTOR(HCF) is defined as if two numbers are given HCF of that number is the highest number that can be divided exactly into all of them.

GIVEN:

Here the numbers which should be divided are given  as 80 and 122

also both of them leave reminders 2 and 5 respectively when divided with HCF(number to be found or largest divident).That also given

SOLUTION:

the remainders are 2 and 5 respectively for dividing 80 and 122

so we should find HIGHEST COMMON FACTOR of 80-2 and 122-5

(as they leave remainder)

HCF of 78 and 117 is 13

(13 is the highest number which divide both 78 and 117)

so the largest number which gives out reminders 2 and 5 when used to divide 80 and 122 is 13

#SPJ3