CBSE Class 10 Answered
Dear Student,
Let that number be K.and let the remainder left when dividing 55, 127 and 175 be x.
therefore we have,
55 = a1k + x (1)
127 = a2k + x (2)
175 = a3 + x (3)
Subtracting (2) from (3), we get
48 = (a3-a2)k
=> k divides 48.
Subtracting (1) from (2), we get
72 = (a2-a1)k
=> k divides 72.
Subtracting (1) from (3), we get
120 = (a3-a1)k
=> k divides 120.
Now the greatest number k will obviously be the gcd of 48, 72 and 120.
By euclid's algorithm, we can easily find out the gcd of (48,72,120) = 24.
Hence, the greatest such number k = 24.
Also the remainder left when dividing 55 = 7.
the remainder left when dividing 127 = 7.
the remainder left when dividing 175 = 7.
Regards Topperlearning.