Which pair of numbers is relatively prime A102 and 321 B.10 and 45 C.3 and 51 D.35 and 72
The Correct Answer and Explanation is:
To determine which pair of numbers is relatively prime, we need to identify pairs of numbers that share no common factors other than 1. Two numbers are relatively prime if their greatest common divisor (GCD) is 1.
Let’s go through each pair:
A. 102 and 321
To find if 102 and 321 are relatively prime, we calculate their GCD:
- Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
- Factors of 321: 1, 3, 7, 21, 17, 51, 102, 321
The common factors are 1, 3, 17, and 51. Since the GCD is 51 (greater than 1), 102 and 321 are not relatively prime.
B. 10 and 45
Let’s find the GCD of 10 and 45:
- Factors of 10: 1, 2, 5, 10
- Factors of 45: 1, 3, 5, 9, 15, 45
The common factors are 1 and 5. Since the GCD is 5 (greater than 1), 10 and 45 are not relatively prime.
C. 3 and 51
Let’s check the GCD of 3 and 51:
- Factors of 3: 1, 3
- Factors of 51: 1, 3, 17, 51
The common factor is 3, so the GCD is 3. Since the GCD is greater than 1, 3 and 51 are not relatively prime.
D. 35 and 72
Finally, let’s check the GCD of 35 and 72:
- Factors of 35: 1, 5, 7, 35
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The only common factor is 1. Since the GCD is 1, 35 and 72 are relatively prime.
Conclusion:
The pair of numbers that is relatively prime is D. 35 and 72.
