Division Rules in Number Systems

Divisibility Rules

• A number is divisible by 9 if the sum of its digits is divisible by 9.
• A number is divisible by 4 if its last two digits are divisible by 4.
• A number is divisible by 3 if the sum of its digits is divisible by 3.

Examples

• When 45342 is divided by 9, the remainder is 0 because the sum of its digits (4+5+3+4+2 = 18) is divisible by 9.
• The number 78276 is fully divisible by 12 because it passes the divisibility rules for 4 (last two digits 76 are divisible by 4) and 3 (sum of all digits 7+8+2+7+6 = 30 is divisible by 3).
• When 5224 is divided by 9, the remainder is 4 because the sum of its digits (5+2+2+4 = 13) leaves a remainder of 4 when divided by 9.
• When 24795 is divided by 9, the remainder is 0 because the sum of its digits (2+4+7+9+5 = 27) is divisible by 9.