Which of the following pairs is NOT coprime?
A(17,34)
B(11, 13)
C(15, 17)
D(17, 23)
Answer:
A. (17,34)
Read Explanation:
Coprime numbers, also known as relatively prime or mutually prime numbers, are pairs of numbers that have only 1 as their greatest common divisor (GCD). This means they share no common factors other than 1.
Examples:
21 and 22 → Factors of 21: {1, 3, 7, 21}, Factors of 22: {1, 2, 11, 22}. Since 1 is the only common factor, they are coprime.
8 and 9 → Factors of 8: {1, 2, 4, 8}, Factors of 9: {1, 3, 9}. Again, only 1 is common, so they are coprime.
Properties:
Any two prime numbers are always coprime (e.g., 3 and 5).
Any two consecutive numbers are always coprime (e.g., 14 and 15).
The numerator and denominator of a simplified fraction are coprime by definition.