check whether the given numbers are divisible by '11' or not? a)786764 b)536393 c)110011 d)1210121 e)758043 f)8338472 g)54678 h)13431 i)423423 j)168861
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Given: the numbers: a)786764 b)536393 c)110011 d)1210121 e)758043 f)8338472 g)54678 h)13431 i)423423 j)168861
To find: whether these numbers are divisible by 11 or not.
Solution:
As we know that the divisibility test for 11 is:
- Divisibility rule for 11: If in any number, the sum of the numbers in the even positions = sum of the odd numbers in the odd positions, then the number is divisible by 11.
- Also, the difference of the sum of the numbers in even positions and the sum of the numbers in the odd positions = 11.
- So now, checking all the numbers for this test:
- a) 786764 = 7+6+6= 8+7+4
- So this number is divisible by 11.
- b)536393 = 5+6+9 ≠ 3+3+3
- So this number is divisible by 11.
- c)110011 = 1+0+1=1+0+1
- So this number is divisible by 11.
- d)1210121= 1+1+1+1= 2+0+2
- So this number is divisible by 11.
- e)758043 = 7+8+4=5+0+3
- So this number is not divisible by 11.
- f)8338472 = 8+3+4+2= 3+8+7
- So this number is not divisible by 11.
- g)54678 = 5+6+8=4+7
- So this number is not divisible by 11.
- h)13431 = 1+4+1 = 3+3
- So this number is divisible by 11.
- i)423423 = 4+3+2= 2+4+3
- So this number is divisible by 11.
- j)168861 = 1+8+6= 6+8+1
- So this number is divisible by 11.
Answer:
So the numbers divisible by 11 are a, b, c, d, h, i, j.
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