Questions: Use the divisibility tests to determine whether 350 is divisible by 2, 3, 5, 6, and 10.

Solution Steps

To determine whether 350 is divisible by 2, 3, 5, 6, and 10, we can use the following divisibility rules:

1. A number is divisible by 2 if its last digit is even.
2. A number is divisible by 3 if the sum of its digits is divisible by 3.
3. A number is divisible by 5 if its last digit is 0 or 5.
4. A number is divisible by 6 if it is divisible by both 2 and 3.
5. A number is divisible by 10 if its last digit is 0.

A number is divisible by 2 if its last digit is even. The last digit of 350 is 0, which is even. Therefore, 350 is divisible by 2. \[ 350 \div 2 = 175 \] \[ \text{Divisible by 2: } \boxed{\text{True}} \]

A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 350 is: \[ 3 + 5 + 0 = 8 \] Since 8 is not divisible by 3, 350 is not divisible by 3. \[ 8 \div 3 \approx 2.6667 \] \[ \text{Divisible by 3: } \boxed{\text{False}} \]

A number is divisible by 5 if its last digit is 0 or 5. The last digit of 350 is 0. Therefore, 350 is divisible by 5. \[ 350 \div 5 = 70 \] \[ \text{Divisible by 5: } \boxed{\text{True}} \]

A number is divisible by 6 if it is divisible by both 2 and 3. From the previous steps, we know that 350 is divisible by 2 but not by 3. Therefore, 350 is not divisible by 6. \[ \text{Divisible by 6: } \boxed{\text{False}} \]

A number is divisible by 10 if its last digit is 0. The last digit of 350 is 0. Therefore, 350 is divisible by 10. \[ 350 \div 10 = 35 \] \[ \text{Divisible by 10: } \boxed{\text{True}} \]

Final Answer