A number is divisible by 5 if its last digit is either 0 or 5. This is a simple rule that works for all whole numbers.
Understanding Divisibility by 5
The divisibility rule for 5 is based on the structure of our decimal number system. Every number can be expressed as a sum of multiples of powers of 10. For example, the number 123 can be written as (1 x 100) + (2 x 10) + (3 x 1). When you divide a multiple of 10 by 5, you always get a whole number. This is because 10 = 5 x 2. Consequently, any number ending in 0 is divisible by 5.
Numbers ending in 5 are also divisible by 5 because they can be expressed as a multiple of 10 plus 5. Since 5 is itself divisible by 5, the entire number is also divisible by 5.
Examples:
- 10: The last digit is 0, so 10 is divisible by 5 (10 / 5 = 2).
- 25: The last digit is 5, so 25 is divisible by 5 (25 / 5 = 5).
- 1005: The last digit is 5, so 1005 is divisible by 5 (1005 / 5 = 201).
- 4320: The last digit is 0, so 4320 is divisible by 5 (4320 / 5 = 864).
- 9995: The last digit is 5, so 9995 is divisible by 5 (9995 / 5 = 1999).
This simple check eliminates the need for actual division, making it a quick and efficient way to determine divisibility by 5. The provided reference explicitly states: "If the last digit is a 5 or a 0, the number is divisible by 5." This directly supports the method described above.
