- Divisibility rules facilitate finding factors of a given number by eliminating the need to divide the number by all of the possible divisor factors
- The application of the divisibility rules are called Divisibility Tests
- Divisibility by 2: All even numbers are divisible by 2 (2 is a prime number)
- Divisibility by 3: If the sum of the digits in a number is divisible by 3, then the number is divisible by 3 (3 is a prime number)
- Divisibility by 4: If the number formed by the last two digits in a number (ones place and tens place) is divisible by 4, then the number is divisible by 4. Additionally, if the quotient resulting from the number being evenly divided by 2 is even, then the number is divisible by 4
- Divisibility by 5: If the last digit in a number (ones place) is either 0 or 5, then it is divisible by 5 (5 is a prime number)
- Divisibility by 8: If the number formed by the last three digits in a number is divisible by 8, then the number is divisible by 8
- Divisibility by 9: If the sum of the digits in a number is divisible by 9, then the number is divisible by 9
- Divisibility by 10: If the last digit in a number is 0, then the number is divisible by 10
- Note: If a number fails a divisibility test, then the number is also not divisible by the multiples of the divisor
- Example: Since the sum of the digits in 262 equals 10 (2 + 6 + 2), 262 is not divisible by 3, and as a result, 262 is not divisible by the multiples of 3 (6, 9, 12, …).
Divisibility_rule (Wikipedia)
A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, or base, and they are all different, this article presents rules and examples only for decimal, or base 10, numbers. Martin Gardner explained and popularized these rules in his September 1962 "Mathematical Games" column in Scientific American.