let n be the largest integer that is the product of exactly 3 distinct prime numbers x, y and 10 x + y where x and y are the digits what is the sum of digits of n
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Given, x and y are digits such that x, y and 10x + y are prime
numbers and their product is n largest possible.
so x = 7 and y = 3 WHY????
since n is largest possible product so choosing x
as largest prime digit i.e 7
and y can’t be 7 as 10x+y would be divisible by 7 but given it is
a prime number and it can’t be 5 also as 10x+y=75 not a prime thus y=3
which makes 10x+y=73 i.e. a prime number as required
Now, n = (7)*(3)*(73) = 1533
hence sum of digits of n = 1+5+3+3=12.
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