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Find the gcd (111....11 hundred ones; 11....11 sixty ones).
- a)111....forty ones
- b)111.....twenty five ones
- c)111..... twenty ones
- d)111.... sixty ones
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Find the gcd (111....11 hundred ones; 11....11 sixty ones).a)111....fo...
Solution:
To solve this problem we need to use the concept of divisibility rules.
Divisibility rule of 11 states that if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a multiple of 11, then the number is divisible by 11.
In this case, both the numbers have only one digit repeated multiple times. Therefore, the sum of digits at odd places and even places will be the same for both numbers.
Hence, we can conclude that the gcd of both numbers will be the smaller number.
a) 111....forty ones
The number of ones is even. Therefore, the sum of digits at odd places and even places will be the same. Hence, the number is divisible by 11.
b) 111.....twenty five ones
The number of ones is odd. Therefore, the sum of digits at odd places and even places will be different. Hence, the number is not divisible by 11.
c) 111..... twenty ones
The number of ones is even. Therefore, the sum of digits at odd places and even places will be the same. Hence, the number is divisible by 11.
d) 111.... sixty ones
The number of ones is even. Therefore, the sum of digits at odd places and even places will be the same. Hence, the number is divisible by 11.
Hence, the gcd of 111....20 ones and 111....60 ones is 111....20 ones.
To solve this problem we need to use the concept of divisibility rules.
Divisibility rule of 11 states that if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a multiple of 11, then the number is divisible by 11.
In this case, both the numbers have only one digit repeated multiple times. Therefore, the sum of digits at odd places and even places will be the same for both numbers.
Hence, we can conclude that the gcd of both numbers will be the smaller number.
a) 111....forty ones
The number of ones is even. Therefore, the sum of digits at odd places and even places will be the same. Hence, the number is divisible by 11.
b) 111.....twenty five ones
The number of ones is odd. Therefore, the sum of digits at odd places and even places will be different. Hence, the number is not divisible by 11.
c) 111..... twenty ones
The number of ones is even. Therefore, the sum of digits at odd places and even places will be the same. Hence, the number is divisible by 11.
d) 111.... sixty ones
The number of ones is even. Therefore, the sum of digits at odd places and even places will be the same. Hence, the number is divisible by 11.
Hence, the gcd of 111....20 ones and 111....60 ones is 111....20 ones.
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Community Answer
Find the gcd (111....11 hundred ones; 11....11 sixty ones).a)111....fo...
The correct option is C 111..... twenty ones
The required GCD would be 1111...111 twenty ones.
The required GCD would be 1111...111 twenty ones.
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