Which of the following are co-prime numbers?
a. 3 and 5
b. 31 and 62
c. 4 and 9
d. 36 and 49
e. 72 and 55
f. 40 and 4
Answer (2)
Co-prime numbers, also known as relatively prime numbers, are two numbers that have no common factors other than 1. In other words, their greatest common divisor (GCD) is 1.
Let's analyze each pair to determine if they are co-prime:
3 and 5
The factors of 3 are 1 and 3. The factors of 5 are 1 and 5.
The only common factor is 1, so 3 and 5 are co-prime.
31 and 62
The factors of 31 are 1 and 31. The factors of 62 are 1, 2, 31, and 62.
The common factors are 1 and 31, so 31 and 62 are not co-prime.
4 and 9
The factors of 4 are 1, 2, and 4. The factors of 9 are 1, 3, and 9.
The only common factor is 1, so 4 and 9 are co-prime.
36 and 49
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 49 are 1, 7, and 49.
The only common factor is 1, so 36 and 49 are co-prime.
72 and 55
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The factors of 55 are 1, 5, 11, and 55.
The only common factor is 1, so 72 and 55 are co-prime.
40 and 4
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The factors of 4 are 1, 2, and 4.
The common factors are 1, 2, and 4, so 40 and 4 are not co-prime.
Answer: The co-prime pairs are: a. 3 and 5, c. 4 and 9, d. 36 and 49, e. 72 and 55.
The co-prime pairs among the given options are 3 and 5, 4 and 9, 36 and 49, and 72 and 55. The pairs 31 and 62, as well as 40 and 4, are not co-prime because they share common factors greater than 1.
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