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GCD & LCMhard
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Let SSS be the set of divisors of n=210⋅35n = 2^{10} \cdot 3^5n=210⋅35. How many pairs of divisors (d1,d2)(d_1, d_2)(d1​,d2​) exist such that gcd(d1,d2)=22⋅31\text{gcd}(d_1, d_2) = 2^2 \cdot 3^1gcd(d1​,d2​)=22⋅31?