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Product of odd primes with distinct digits (Posted on 2021-07-23) Difficulty: 2 of 5
(1): Consider the set of the smallest 6 odd primes: {3,5,7,11,13,17}.
What is the largest multiple of this product which has distinct digits ?

(2) What is the maximum number of digits a square-free integer (whether even or odd) can have if its digits are all distinct?

(3) What is the largest odd square-free integer with distinct digits having exactly n prime factors for n = 1,2,3,4,5? You can extend this to larger numbers of factors if you wish.

Note: a square-free integer is one whose prime factorization has exactly one factor for each prime that appears in it.

See The Solution Submitted by Larry    
Rating: 5.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Brian and Charlie: note a few details | Comment 4 of 5 |
(In reply to Brian and Charlie: note a few details by Larry)

>> prod(primes(17))/2
ans =
      255255   (the product of the first 6 odd primes)


9527648130     =    37326   *    255255

  Posted by Charlie on 2021-07-27 21:56:47
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