Question

The greatest number that will divide 63, 138 and 228 so as to leave the same remainder in each case:
(a) 15
(b) 20
(c) 35
(4) 40

Answer 1

hi
here is your answer ✌️
138-63 =75
228-138=90
hcf of 75 and 90 is 15
so the answer is 15
hope this help you plz
marks as brainliest answer

Answer 2

answer : option (a) 15

explanation : we have to find greatest number that will divide 63, 138 and 228 so as to leave the same remainder in each cases.

greatest number = HCF of (138 - 63) and (228 - 138)

= HCF of 75 and 90 [ as 138 - 63 = 75 and 228 - 138 = 90 ]

= 15

hence, greatest number is 15.

method 2 :- from Euclid algorithm,

we can write all given numbers into a = bq + r ,

so, 63 = 15 × 4 + 3

138 = 15 × 7 + 3

228 = 15 × 15 + 3

here it is clear that, 4, 7, 15 are not divisible with each other. and also remainder is 3 in each case. hence, 15 is the greatest number.

hence, option (a) is correct .