Find, without dividing, whether the following numbers are divisible by 9.
123
Not divisible by 9. Sum of digits = 1 + 2 + 3 = 6, which is not divisible by 9.
405
Divisible by 9. Sum of digits = 4 + 0 + 5 = 9, which is divisible by 9.
8888
Not divisible by 9. Sum of digits = 8 + 8 + 8 + 8 = 32, which is not divisible by 9.
93547
Not divisible by 9. Sum of digits = 9 + 3 + 5 + 4 + 7 = 28, which is not divisible by 9.
358095
Not divisible by 9. Sum of digits = 3 + 5 + 8 + 0 + 9 + 5 = 30, which is not divisible by 9.
Explanation
(i) The chapter states that a number is divisible by 9 if the sum of its digits is divisible by 9. Since 6 is not divisible by 9, 123 is not divisible by 9. (ii) The sum of digits equals 9, which is divisible by 9. Therefore, 405 is divisible by 9. (iii) The sum of digits is 32. Since 32 is not divisible by 9 (32 ÷ 9 = 3 remainder 5), 8888 is not divisible by 9. (iv) The sum of digits is 28. Since 28 is not divisible by 9, 93547 is not divisible by 9. (v) The sum of digits is 30. Since 30 is not divisible by 9, 358095 is not divisible by 9.