A Pre-RMO question! -14

Number Theory Level 1

Let n n be the largest integer that is product of three primes - x , y x,y and 10 x + y 10x+y ; where x , y x,y are single digit numbers. What is the sum of the digits of n n ?


The answer is 12.

Zakir Husain by Zakir Husain , 41, India

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1 solution

Mahdi Raza
Jun 12, 2020
  • The largest product will be formed when 10 x + y 10x + y is the largest. Finding numbers from sieve of erasthoneses, in reverse: we find 73 73 as the largest number that has both digits prime.
  • According to this: N = 7 × 3 × 73 = 1533 N = 7 \times 3 \times 73 = 1533
  • Sum of digits of N N is 1 + 5 + 3 + 3 = 12 1 + 5 + 3 + 3 = \boxed{12}
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