Which pair is not coprime?
8, 10
11, 12
1, 3
31, 33
Meaning of coprime: Two numbers are coprime if their greatest common divisor (gcd) is 1.
Check each option.
Option A: 8 and 10
Factors of 8: \(1, 2, 4, 8\)
Factors of 10: \(1, 2, 5, 10\)
Common factors: \(1, 2\)
Greatest common divisor: \(\gcd(8,10) = 2\)
Since \(2 \ne 1\), they are not coprime.
Option B: 11 and 12
\(11\) is prime. \(12 = 2^2 \times 3\).
No common factor greater than 1, so \(\gcd(11,12)=1\) ⇒ coprime.
Option C: 1 and 3
\(\gcd(1,3)=1\) ⇒ coprime. (1 is coprime with every number.)
Option D: 31 and 33
\(31\) is prime. \(33 = 3 \times 11\).
31 is not 3 or 11, so \(\gcd(31,33)=1\) ⇒ coprime.
Conclusion: Only Option A has gcd not equal to 1.