- 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, …).