Class 5 Exam > Class 5 Questions > Which of these are co-prime(a) 16,18(b) 11,48...
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Which of these are co-prime
(a) 16,18
(b) 11,48
(c) 8,23
(a) 16,18
(b) 11,48
(c) 8,23
- a)b and c
- b)b
- c)a
- d)a and c
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Which of these are co-prime(a) 16,18(b) 11,48(c) 8,23a)b and cb)bc)ad)...
In number theory, Co-prime numbers are those numbers if the only positive factor that divides them is 1.
Here,
Option A: (16,18) Factors that divide both of them are 1,2.
Option B: (11,48) Factor that divides both of them is 1.
Option C: (8,23) Factor that divides both of them is 1.
In reference to above definition both b and c are co-prime numbers.
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Community Answer
Which of these are co-prime(a) 16,18(b) 11,48(c) 8,23a)b and cb)bc)ad)...
To determine if two numbers are co-prime, we need to find their greatest common divisor (GCD). If the GCD of two numbers is 1, then the numbers are co-prime.
Now let's check each option:
(a) 16,18: To find the GCD, we can use the Euclidean algorithm.
16 ÷ 18 = 0 remainder 16
18 ÷ 16 = 1 remainder 2
16 ÷ 2 = 8
2 ÷ 8 = 0 remainder 2
The GCD of 16 and 18 is 2, so they are not co-prime.
(b) 11,48:
11 ÷ 48 = 0 remainder 11
48 ÷ 11 = 4 remainder 4
11 ÷ 4 = 2 remainder 3
4 ÷ 3 = 1 remainder 1
3 ÷ 1 = 3
1 ÷ 3 = 0 remainder 1
The GCD of 11 and 48 is 1, so they are co-prime.
(c) 8,23:
8 ÷ 23 = 0 remainder 8
23 ÷ 8 = 2 remainder 7
8 ÷ 7 = 1 remainder 1
7 ÷ 1 = 7
1 ÷ 7 = 0 remainder 1
The GCD of 8 and 23 is 1, so they are co-prime.
From the above analysis, we can conclude that the co-prime pairs are:
(b) 11, 48
(c) 8, 23
Therefore, the correct answer is option (a) b and c.
Now let's check each option:
(a) 16,18: To find the GCD, we can use the Euclidean algorithm.
16 ÷ 18 = 0 remainder 16
18 ÷ 16 = 1 remainder 2
16 ÷ 2 = 8
2 ÷ 8 = 0 remainder 2
The GCD of 16 and 18 is 2, so they are not co-prime.
(b) 11,48:
11 ÷ 48 = 0 remainder 11
48 ÷ 11 = 4 remainder 4
11 ÷ 4 = 2 remainder 3
4 ÷ 3 = 1 remainder 1
3 ÷ 1 = 3
1 ÷ 3 = 0 remainder 1
The GCD of 11 and 48 is 1, so they are co-prime.
(c) 8,23:
8 ÷ 23 = 0 remainder 8
23 ÷ 8 = 2 remainder 7
8 ÷ 7 = 1 remainder 1
7 ÷ 1 = 7
1 ÷ 7 = 0 remainder 1
The GCD of 8 and 23 is 1, so they are co-prime.
From the above analysis, we can conclude that the co-prime pairs are:
(b) 11, 48
(c) 8, 23
Therefore, the correct answer is option (a) b and c.
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