(2301)

We first note that the number of +ve divisors of a +ve integer n is (a 1 + 1) (a 2 + 1)....(a k + 1)

If n = .....

where p 1 ......,p k are integers.

Now, a = 10 40 = 2 40 5 40 ; b = 20 30 = 2 60 5 30

gcd of a, b is c = 2 40 5 30

Let A, B denote the sets of divisor of a, b respectively.

Then A ∩ B is set of divisors of c.

|A| = 41 2 ; |B| = 61 × 31 ; |A ∩ B| =41 × 31

Hence |A ∪ B| = 1681 + 1891 – 1271 = 2301

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