Find, without dividing, whether the following numbers are divisible by 9.
123
123 is not divisible by 9. The sum of digits is 1 + 2 + 3 = 6, which is not divisible by 9.
405
405 is divisible by 9. The sum of digits is 4 + 0 + 5 = 9, which is divisible by 9.
8888
8888 is not divisible by 9. The sum of digits is 8 + 8 + 8 + 8 = 32, which is not divisible by 9.
93547
93547 is not divisible by 9. The sum of digits is 9 + 3 + 5 + 4 + 7 = 28, which is not divisible by 9.
358095
358095 is not divisible by 9. The sum of digits is 3 + 5 + 8 + 0 + 9 + 5 = 30, which is not divisible by 9.
Explanation
(i) Using the divisibility rule for 9: Sum of digits = 1 + 2 + 3 = 6. Since 6 is not divisible by 9, the number 123 is not divisible by 9. (ii) Using the divisibility rule for 9: Sum of digits = 4 + 0 + 5 = 9. Since 9 is divisible by 9, the number 405 is divisible by 9. (iii) Using the divisibility rule for 9: Sum of digits = 8 + 8 + 8 + 8 = 32. Since 32 is not divisible by 9, the number 8888 is not divisible by 9. (iv) Using the divisibility rule for 9: Sum of digits = 9 + 3 + 5 + 4 + 7 = 28. Since 28 is not divisible by 9, the number 93547 is not divisible by 9. (v) Using the divisibility rule for 9: Sum of digits = 3 + 5 + 8 + 0 + 9 + 5 = 30. Since 30 is not divisible by 9, the number 358095 is not divisible by 9.