# 935 Is the Second Lucas-Carmichael Number

935 = 5 × 11 × 17, and 935 + 1 is evenly divisible by 5 + 1, 11 + 1, and 17 + 1. That makes 935 only the SECOND Lucas-Carmichael number. Thanks to Stetson.edu for that fun fact.

Today’s puzzle is a level 3, a good transition from the easier puzzles to the more difficult ones. Print the puzzles or type the solution on this excel file: 10-factors-932-941

Here’s more about the number 935:

935 is the sum of the nineteen prime numbers from 13 to 89.

935 is the hypotenuse of four Pythagorean triples:
143-924-935, which is 11 times (13-84-85)
396-847-935, which is 11 times (36-77-85)
440-825-935, which is (8-15-17) times 55
561-748-935, which is (3-4-5) times 187

• 935 is a composite number.
• Prime factorization: 935 = 5 × 11 × 17
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 935 has exactly 8 factors.
• Factors of 935: 1, 5, 11, 17, 55, 85, 187, 935
• Factor pairs: 935 = 1 × 935, 5 × 187, 11 × 85, or 17 × 55
• 935 has no square factors that allow its square root to be simplified. √935 ≈ 30.5777697 