Which of the following numbers are divisible by both 9 and 11
Which of the following numbers are divisible by both 9 and 11
The correct option is A 1089
To check the divisibility of a number by 11, we find the difference between the sum of the digits at odd place (from the right) and the sum of the digits at even place (from the right) of the number. If the difference is 0 or divisible by 11, then the number is divisible by 11.
1089 ; Sum of the digit in the odd places = 1 + 8 = 9 and sum of the digit in the even places = 9+ 0 = 9
Since the difference is 0 , the number is divisible by 11
For divisibility by 9: if the sum of the digits of a number is divisible by 9, then the number is divisible by 9.
The sum of the digits = 1 + 0 + 8 + 9 = 18 ;divisible by 9 ; Hence 1089 is divisible by 9
Hence 1089 is divisible by both 11 and 9
121 ; The sum of the digit in the odd places = 1 + 1 = 2 and sum of the digit in the even places = 2
2 -2 = 0 ; Hence 121 is divisible by 11
121 ; Sum of the digits is 1 + 2 +1 = 4 ; which is not divisible by 9
Hence 121 is divisible by 11 but not by 9
720; The sum of the digit in the odd places = 7 + 0 = 7 and the sum of the digit in the even places = 0
Since the difference is 7 - 0 ; which is not divisible by 11, hence 720 is not divisible by 11
The sum of the digits = 7 + 2 + 0 = 9 ; which is divisible by 9
∴ 720 is divisible by 9 but not by 11
456 ; The sum of the digit in the odd places = 4 + 6 = 10 and the sum of the digit in the even places = 5
Since the difference between the odd and even places is 10 - 5= 5 ; its not divisible by 11
4 + 5 + 6 = 15 which is not divisible by 9
Hence 456 is not divisible by both 11 and 9
1089
To check the divisibility of a number by 11, we find the difference between the sum of the digits at odd place (from the right) and the sum of the digits at even place (from the right) of the number. If the difference is 0 or divisible by 11, then the number is divisible by 11.
1089 ; Sum of the digit in the odd places = 1 + 8 = 9 and sum of the digit in the even places = 9+ 0 = 9
Since the difference is 0 , the number is divisible by 11
For divisibility by 9: if the sum of the digits of a number is divisible by 9, then the number is divisible by 9.
The sum of the digits = 1 + 0 + 8 + 9 = 18 ;divisible by 9 ; Hence 1089 is divisible by 9
Hence 1089 is divisible by both 11 and 9
121 ; The sum of the digit in the odd places = 1 + 1 = 2 and sum of the digit in the even places = 2
2 -2 = 0 ; Hence 121 is divisible by 11
121 ; Sum of the digits is 1 + 2 +1 = 4 ; which is not divisible by 9
Hence 121 is divisible by 11 but not by 9
720; The sum of the digit in the odd places = 7 + 0 = 7 and the sum of the digit in the even places = 0
Since the difference is 7 - 0 ; which is not divisible by 11, hence 720 is not divisible by 11
The sum of the digits = 7 + 2 + 0 = 9 ; which is divisible by 9
∴ 720 is divisible by 9 but not by 11
456 ; The sum of the digit in the odd places = 4 + 6 = 10 and the sum of the digit in the even places = 5
Since the difference between the odd and even places is 10 - 5= 5 ; its not divisible by 11
4 + 5 + 6 = 15 which is not divisible by 9
Hence 456 is not divisible by both 11 and 9
