611 is the sum of 13 consecutive numbers:

41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 = 611

611 is the sum of 13 consecutive odd numbers:

35 + 37 + 39 + 41 + 43 + 45 + 47 + 49 + 51 + 53 + 55 + 57 + 59 = 611

611 is the sum of the fifteen prime numbers from 13 to 71, a set of numbers that includes all the prime factors of 611.

611 is also the hypotenuse of the Pythagorean triple 235-564-611. What is the greatest common factor of those three numbers?

If you average 13 and 47 (two odd numbers in a factor pair of 611), you get 30 which is 17 numbers away from either factor. That means that (30^2) – (17^2) = 611.

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Today’s puzzle starts off easy enough, but it might get a bit tricky to complete.

Print the puzzles or type the solution on this excel file: 12 Factors 2015-09-07

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• 611 is a composite number.
• Prime factorization: 611 = 13 x 47
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 611 has exactly 4 factors.
• Factors of 611: 1, 13, 47, 611
• Factor pairs: 611 = 1 x 611 or 13 x 47
• 611 has no square factors that allow its square root to be simplified. √611 ≈ 24.718414.

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