1
Question
The remainder when 7×19 is divided by 6 is ________.
The remainder when 7×19 is divided by 6 is ________.
Open in App
Solution
The correct option is A 1
By the theorem on modulo operations, if a, b, c and d are integers and m is a positive integer such that if a≡b(mod m) and c≡d(mod m) , then
(a×c)≡(b×d)(mod m)
Applying the above concept here,
7≡1(mod 6)...(As when 7 will be divide by 6, we get 1 as remainder)
Similarly, we have
19≡1(mod 6)
Hence, 7×19≡1×1(mod 6)
7×19≡1(mod 6)
Remainder = 1
By the theorem on modulo operations, if a, b, c and d are integers and m is a positive integer such that if a≡b(mod m) and c≡d(mod m) , then
(a×c)≡(b×d)(mod m)
Applying the above concept here,
7≡1(mod 6)...(As when 7 will be divide by 6, we get 1 as remainder)
Similarly, we have
19≡1(mod 6)
Hence, 7×19≡1×1(mod 6)
7×19≡1(mod 6)
Remainder = 1
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
