Ask AI: Test the following number for divisibility by 5, 6 and 11. Give a clear explanation. (Do not divide or factorise). 68 979

Sure, let's test the number 68,979 for divisibility by 5, 6, and 11 using their specific rules: ### Divisibility by 5: A number is divisible by 5 if and only if its last digit is 0 or 5. - **Last digit of 68,979**: 9 - Since 9 is neither 0 nor 5, **68,979 is not divisible by 5**. ### Divisibility by 6: A number is divisible by 6 if and only if it is divisible by both 2 and 3. - **Divisibility by 2**: A number is divisible by 2 if its last digit is even. - Last digit of 68,979 is 9, which is not even. - Therefore, **68,979 is not divisible by 2**. - **Divisibility by 3**: A number is divisible by 3 if the sum of its digits is divisible by 3. - Sum of digits of 68,979: \( 6 + 8 + 9 + 7 + 9 = 39 \). - 39 is divisible by 3 (since \( 3 + 9 = 12 \), and 12 is divisible by 3). To be divisible by 6, it must be divisible by both 2 and 3. Since 68,979 is not divisible by 2, **it is not divisible by 6**. ### Divisibility by 11: A number is divisible by 11 if the alternating sum of its digits is divisible by 11. - **Alternating sum of digits of 68,979**: - \( 6 - 8 + 9 - 7 + 9 = 9 - 16 + 9 = 2 \) Since 2 is not divisible by 11, **68,979 is not divisible by 11**. ### Summary: - 68,979 is **not divisible by 5**, **not divisible by 6**, and **not divisible by 11**.