what is the remainder of 74 divided by 7

Guri Bee

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20-10-2024

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Unraveling the Remainder: 74 Divided by 7

Understanding remainders is a fundamental concept in mathematics, often used in applications like time calculations, number theory, and computer programming. In this article, we'll explore the remainder of 74 divided by 7, breaking down the process and highlighting its significance.

The Question:

What is the remainder when 74 is divided by 7?

The Answer:

The remainder of 74 divided by 7 is 2.

Explanation:

• Division: Division involves splitting a whole into equal parts. In this case, we are dividing 74 into groups of 7.
• Quotient: The quotient is the number of times the divisor (7) goes into the dividend (74). We find that 7 goes into 74 ten times (10 x 7 = 70).
• Remainder: The remainder is the amount left over after the division is complete. Since 70 is less than 74, we have a remainder of 4 (74 - 70 = 4). However, this remainder is larger than our divisor (7). We can further divide the remainder (4) by 7, which goes in zero times. This leaves us with a final remainder of 2.

Practical Applications:

Understanding remainders can be applied in various scenarios:

• Time: If a movie starts at 7:00 PM and lasts 105 minutes, the remainder when 105 is divided by 60 (minutes in an hour) tells us the movie ends 45 minutes past the hour (105 / 60 = 1 remainder 45).
• Computer Programming: Remainders are used in algorithms for tasks like finding prime numbers or generating random sequences.

Going Deeper:

• Modular Arithmetic: The concept of remainders forms the basis of modular arithmetic, a branch of mathematics that deals with remainders after division. It has applications in cryptography and computer science.
• Remainder Theorem: This theorem in algebra states that the remainder when a polynomial is divided by a linear expression is equal to the value of the polynomial at the root of the linear expression.

Conclusion:

By understanding the process of division and the concept of remainders, we can efficiently solve problems related to dividing numbers and gain insights into their applications in various fields.