Divisibility of 73428 by 8: A Step-by-Step Guide
The concept of checking divisibility without performing direct division can be a useful skill for many mathematical applications. In this article, we will explore the divisibility of 73428 by 8 and how to determine it without resorting to traditional long division or a calculator. This method involves breaking down the number and using properties of modulo operations to simplify the process.
Understanding the Problem
The problem at hand is to determine whether 73428 is divisible by 8. Instead of performing a long division, we can use the properties of modulo operations to simplify the process. Modulo operation, denoted by mod, gives the remainder when one number is divided by another. In this case, we are interested in the remainder when 73428 is divided by 8.
The Strategy and Breakdown
To simplify the process, we can break down the number 73428 into smaller parts and use the properties of modulo operations. The number 73428 can be written as:
We can further break it down as:
Thus, the original number 73428 can be expressed as:
Knowing that 8 is a factor of 1000 and 400, we can simplify the modulo operation as:
Since 731000 and 400 are both divisible by 8 (as they are multiples of 1000 and 400, respectively), their modulo operations will be zero.
Now, we need to find 28 mod 8:
Therefore, the remainder when 73428 is divided by 8 is 4. This means that 73428 is not divisible by 8.
Conclusion
In conclusion, the divisibility of 73428 by 8 can be determined by breaking down the number and using the properties of modulo operations. By recognizing that the number can be expressed as the sum of parts that are divisible by 8, we can simplify the process and find the remainder without performing extensive calculations. This method can be applied to similar problems to check for divisibility by other numbers.
Related Keywords
divisibility by 8: A method to determine if a number can be divided by 8 without leaving a remainder.
modulo operation: A mathematical operation that finds the remainder after a division of one number by another.
division without long division: Techniques to determine divisibility of a number without performing long division, using properties of modulo operations.