Questions: Use the divisibility tests to determine whether 350 is divisible by 2, 3, 5, 6, and 10.
Transcript text: Question
Use the divisibility tests to determine whether 350 is divisible by $2,3,5,6$, and 10 .
Solution
Solution Steps
To determine whether 350 is divisible by 2, 3, 5, 6, and 10, we can use the following divisibility rules:
A number is divisible by 2 if its last digit is even.
A number is divisible by 3 if the sum of its digits is divisible by 3.
A number is divisible by 5 if its last digit is 0 or 5.
A number is divisible by 6 if it is divisible by both 2 and 3.
A number is divisible by 10 if its last digit is 0.
Step 1: Check Divisibility by 2
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.
\[ 350 \div 2 = 175 \]
\[ \text{Divisible by 2: } \boxed{\text{True}} \]
Step 2: Check Divisibility by 3
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.
\[ 8 \div 3 \approx 2.6667 \]
\[ \text{Divisible by 3: } \boxed{\text{False}} \]
Step 3: Check Divisibility by 5
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.
\[ 350 \div 5 = 70 \]
\[ \text{Divisible by 5: } \boxed{\text{True}} \]
Step 4: Check Divisibility by 6
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.
\[ \text{Divisible by 6: } \boxed{\text{False}} \]
Step 5: Check Divisibility by 10
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.
\[ 350 \div 10 = 35 \]
\[ \text{Divisible by 10: } \boxed{\text{True}} \]