Which of the following pair of numbers is relatively prime to each other?

Two numbers are relatively prime (coprime) when they have no common factors except 1. This means their Greatest Common Divisor (GCD) = 1.

For each pair, find the GCD. If GCD = 1, the numbers are relatively prime. If GCD > 1, they are not relatively prime.

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Option 1: (371, 159)

Using the Euclidean Algorithm:

371 ÷ 159 = 2 remainder 53

159 ÷ 53 = 3 remainder 0

GCD = 53 (NOT relatively prime)

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Option 2: (407, 259)

407 ÷ 259 = 1 remainder 148

259 ÷ 148 = 1 remainder 111

148 ÷ 111 = 1 remainder 37

111 ÷ 37 = 3 remainder 0

GCD = 37 (NOT relatively prime)

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Option 3: (95, 112)

95 is odd (ends in 5) and 112 is even (ends in 2), so they don't share the factor 2.

95 = 5 × 19

112 = $2^4$ × 7

No common factors exist.

GCD = 1 (RELATIVELY PRIME)

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Option 4: (57, 123)

Both are divisible by 3:

Sum of digits of 57: 5 + 7 = 12 (divisible by 3)

Sum of digits of 123: 1 + 2 + 3 = 6 (divisible by 3)

GCD = 3 (NOT relatively prime)

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The answer is Option 3: (95, 112)

These numbers share no common factors except 1, making them relatively prime.