When an integer m is divided by 6, the remainder is 4. What is the remainder when 7m is divided by 3?

Question: When an integer m is divided by 6, the remainder is 4. What is the remainder when 7m is divided by 3?

Solution:
m = 6 × quotient + remainder
or, m = 6n + 4 [Let, quotient = n]
or, 7m = 7 × 6n + 7 × 4
or, 7m = 7 × 6n + 28

since remainder can not be greater than or equal to divisor
= 6 ×(7n) + 27 + 1
= 3(14n + 9) + 1

if this number is divided by 3 the remainder will be 1

∴ Remainder is 1