Which pair of these numbers is coprime?
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A.
4, 12
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B.
33, 35
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C.
15, 9
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D.
45, 9
Correct Answer:
B. 33, 35
Explanation:
Two numbers are considered coprime (or relatively prime) if their greatest common divisor (GCD) is 1, meaning they share no common factors other than 1. To find the correct pair, we examine the factors of each option: - 4 and 12: Both are divisible by 2 and 4. Since their GCD is 4, they are not coprime. - 33 and 35: The factors of 33 are 1, 3, 11, and 33. The factors of 35 are 1, 5, 7, and 35. Their only common factor is 1, making them coprime. - 15 and 9: Both are divisible by 3. Since their GCD is 3, they are not coprime. - 45 and 9: Both are divisible by 3 and 9. Since 9 is a factor of 45, their GCD is 9, so they are not coprime.Therefore, the pair (33, 35) is the only coprime set because 1 is the only positive integer that divides both numbers.
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