"True or fals: a number is divisible by 8 if it is divisble by 4 and divisible by 2?" Yes, but it is false. If the two numbers are prime to each other, then this logic will work. There are not many common factors between the two numbers. For example, it is true to say that a number is divisible by 6 if it is divisible by 3 and divisible by 2. If the number 3A2B needs to be divisible by 6 (where A and B stand for undertermined digits), then it has to be divisible by 3 and divisible by 2. The rule of divisibility for 2 is that the last digit (B) must be even. The rule of divisibility for 3 is that the sum of all digits must be divisible by 3. For each possible value of B, enumerate the possibilities for A and A. A=0 B=1 (3120), B=4 (3420) B=7 (3720) A=2 B=2 (3222), B=5 (3522) B=8 (3822) A=4 Is there anything else you would like to see? A=6 Is there anything else you would like to see? A=8 Is there anything else you would like to see? How many different things can be done?