Question

33. A competition question requests students to form a three-digit number.

In this question, the following conditions are given.
The digits in the number must be different.
All the digits in the numbers must be prime numbers.
The number formed must be the product of four prime numbers.
The sum of the prime factors of the number is 30.
What is the three-digit number?

Answer 1

532

Explanation:

532 = 2·2·7·19

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There are 24 possible 3-digit numbers from the set {2, 3, 5, 7}. Of those, 6 have four factors: 372, 375, 532, 572, 732, 735.

The sums of factors of these numbers are ...

38, 18, 30, 28, 68, 22

The number of interest is 532.