Divisibility rule by 11
If the sum of the digits in the odd places and the sum of the digits in the even places difference is a multiple of 11 or zero then we can say that the given number is divisible by 11.
Example: Is 1023
divisible by 11?
Solution:
Sum of the digits in the odd
places (Black Color) = 1 + 2 = 3
Sum of the digits in the
even place (Red Color) = 0 + 3 = 3
Difference between the two
sums = 3 - 3 = 0
Hence, 1023 is divisible by 11.
Example: Is 1749
divisible by 11?
Solution:
Sum of the digits in the odd
places (Black Color) = 1 + 4 = 5
Sum of the digits in the
even place (Red Color) = 7 + 9 = 16
Difference between the two
sums = 16 - 5 = 11
Hence, 1749 is divisible by 11.
Example: Is 592845
divisible by 11?
Solution:
Sum of the digits in the odd
places (Black Color) = 5 + 2 + 4 = 11
Sum of the digits in the
even place (Red Color) = 9 + 8 + 5 = 22
Difference between the two
sums = 22 - 11 = 11
Hence, 592845 is divisible by 11.
Example: Is 694201
divisible by 11?
Solution:
Sum of the digits in the odd
places (Black Color) = 6 + 4 + 0 = 10
Sum of the digits in the
even place (Red Color) = 9 + 2 + 1 = 12
Difference between the two
sums = 12 - 10 = 2
Hence, 694201 is not divisible by 11.
Let’s have practice of divisibility rule by 11:
Which of the following numbers are divisible by
11?
852346, 45982, 326117, 85932, 6987751, 5676
Solution:
852346 = [8 + 2 + 4 =14
& 5 + 3 + 6 = 14] 14 – 14 = 0 Hence, divisible by 11
45982 = [4 + 9 + 2 =15 &
5 + 8 = 13] 15 – 13 = 2 Hence, not divisible by 11
326117 = [3 + 6 + 1 =10
& 2 + 1 + 7 = 10] 10 – 10 = 0 Hence, divisible by 11
85932 = [8 + 9+ 2 = 19 &
5 + 3 = 8] 19 – 8 = 11 Hence, divisible by 11
698775 = [6 + 8 + 7 =21
& 9 + 7 + 5 = 21] 21 – 21 = 0 Hence, divisible by 11
5676 = [5 + 7 =12 & 6 +
6 = 12] 12 – 12 = 0 Hence, divisible by 11
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