Final answer:
The remainder of 74 divided by 7 is 4, calculated by subtracting 70 from 74, which represents the 10 complete groups of 7 in 74.
Step-by-step explanation:
When dividing 74 by 7, the quotient is 10, and the remainder is 4. This result is obtained by dividing 74 by 7 using long division. The divisor, 7, goes into 74 ten times, yielding 70. However, there is a remaining amount of 4 that cannot be evenly divided by 7. Therefore, the complete expression is
74=7×10+4
74=7×10+4, where 10 is the quotient and 4 is the remainder.
Understanding remainders is essential in various mathematical contexts. In modular arithmetic, for instance, remainders play a crucial role. They help establish congruence relationships and are fundamental in solving equations and analyzing patterns. Additionally, in computer science, algorithms often leverage the concept of remainders for tasks such as indexing, hashing, and optimizing repetitive calculations, showcasing the practical significance of this mathematical concept beyond traditional arithmetic.