Ask AI: Test the following numbers for divisibility by 5, 6 and 11(Do not divide or factorise). a) 98 98 789 350 b) 76 885 976 256

To test for divisibility by 5, 6, and 11 without directly dividing or factoring, we need to apply the specific rules for each type of divisibility. ### Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5. - **98 98 789 350**: The last digit is 0. Therefore, it is divisible by 5. - **76 885 976 256**: The last digit is 6. Therefore, it 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 (0, 2, 4, 6, or 8). - **Divisibility by 3**: A number is divisible by 3 if the sum of its digits is a multiple of 3. **98 98 789 350**: - Last digit is 0 (even), so it is divisible by 2. - Sum of digits = 9 + 8 + 9 + 8 + 7 + 8 + 9 + 3 + 5 + 0 = 66. The sum 66 is divisible by 3 (because 6 + 6 = 12 and 1 + 2 = 3, which is divisible by 3). Therefore, 98 98 789 350 is divisible by 6. **76 885 976 256**: - Last digit is 6 (even), so it is divisible by 2. - Sum of digits = 7 + 6 + 8 + 8 + 5 + 9 + 7 + 6 + 2 + 5 + 6 = 69. The sum 69 is divisible by 3 (because 6 + 9 = 15 and 1 + 5 = 6, which is divisible by 3). Therefore, 76 885 976 256 is divisible by 6. ### Divisibility by 11: A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is a multiple of 11 (including 0). **98 98 789 350**: - Odd-positioned digits: 9, 9, 8, 8, 9 (sum = 9 + 9 + 8 + 8 + 9 = 43). - Even-positioned digits: 8, 7, 9, 3, 0 (sum = 8 + 7 + 9 + 3 + 0 = 27). The difference is |43 - 27| = 16. Since 16 is not a multiple of 11, 98 98 789 350 is not divisible by 11. **76 885 976 256**: - Odd-positioned digits: 7, 8, 8, 9, 7, 2, 6 (sum = 7 + 8 + 8 + 9 + 7 + 2 + 6 = 47). - Even-positioned digits: 6, 5, 9, 7, 6, 5 (sum = 6 + 5 + 9 + 7 + 6 + 5 = 38). The difference is |47 - 38| = 9. Since 9 is not a multiple of 11, 76 885 976 256 is not divisible by 11. ### Summary: - **98 98 789 350**: Divisible by 5 and 6, but not by 11. - **76 885 976 256**: Divisible by 6, but not by 5 or 11.