How Do You Know That a Number Can Be Divided by 5?
A number is divisible by 5 if its last digit is either 0 or 5. This simple rule allows for quick determination of divisibility without performing the actual division.
The divisibility rule for 5 is based on the structure of the decimal number system. Every number can be expressed as a sum of multiples of powers of 10. For example, the number 475 can be written as:
475 = 400 + 70 + 5 = (4 × 100) + (7 × 10) + (5 × 1)
Since 10 is divisible by 5 (10 = 5 × 2), any multiple of 10 is also divisible by 5. Therefore, the terms (4 × 100) and (7 × 10) are both divisible by 5. The divisibility of the entire number 475 then depends solely on the last digit, which is 5, and is also divisible by 5.
Examples
- 125: The last digit is 5, so 125 is divisible by 5 (125 ÷ 5 = 25).
- 300: The last digit is 0, so 300 is divisible by 5 (300 ÷ 5 = 60).
- 872: The last digit is 2, so 872 is not divisible by 5.
- 9,505: The last digit is 5, so 9,505 is divisible by 5 (9,505 ÷ 5 = 1901).
Practical Applications
This rule is extremely useful in various situations:
- Mental Math: Quickly determine if a number is divisible by 5 without using a calculator.
- Number Theory: Used in more complex divisibility problems and algorithms.
- Programming: Easily implemented in code to check for divisibility by 5.
This simple test provides a fast and efficient way to determine the divisibility of any number by 5. As noted in several sources such as Cuemath, Wikipedia, and many others, checking the last digit is the key to determining if a number is divisible by 5.
