If s1= {1,2,3,4,.....,23} & s2={207,208,209,210,.....,691}, how many elements of the set s2 are divisible by at least four distinct prime numbers that are elements of the set s1?

1.9
2.8
3.11
4.12

• If a number of the set S2 is divisible by at least four distinct prime numbers of the set S1, then it will be divisible by their product as well.
  The number of numbers in S2 divisible by the product of 2, 3, 5 and 7, i.e. 210 = 3.
  The number of numbers in S2 divisible by the product of 2, 3, 5 and 11, i.e. 330 = 2.
  The number of numbers in S2 divisible by the product of 2, 3, 5 and 13, i.e. 390 = 1.
  The number of numbers in S2 divisible by the product of 2, 3, 5 and 17, i.e. 510 = 1.
  The number of numbers in S2 divisible by the product of 2, 3, 5 and 19, i.e. 570 = 1.
  The number of numbers in S2 divisible by the product of 2, 3, 5 and 23, i.e. 690 = 1.
  The number of numbers in S2 divisible by the product of 2, 3, 7 and 11, i.e. 462 = 1.
  The number of numbers in S2 divisible by the product of 2, 3, 7 and 13, i.e. 546 = 1.
  There is no other combination of four or more prime
  numbers in set S1 that divides any of the elements of set S2.
  Hence, the required number of elements = 11.
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