1311

1311 Little Square Candies

/ ivasallay / Leave a comment

Here’s a puzzle made with some sweet squares. The nine clues in it are all you need to find the factors and complete the entire “mixed-up” multiplication table. 

Print the puzzles or type the solution in this excel file: 12 factors 1311-1319

Now I’ll write some facts about the number 1311:

  • 1311 is a composite number.
  • Prime factorization: 1311 = 3 × 19 × 23
  • 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 1311 has exactly 8 factors.
  • Factors of 1311: 1, 3, 19, 23, 57, 69, 437, 1311
  • Factor pairs: 1311 = 1 × 1311, 3 × 437, 19 × 69, or 23 × 57
  • 1311 has no square factors that allow its square root to be simplified. √1311≈ 36.20773

1311 is the sum of five consecutive prime numbers:
251 + 257 + 263 + 269 + 271 = 1311

As shown in their factor trees below, 1308, 1309, 1310, and 1311 each have three distinct prime numbers in their prime factorizations. They are the smallest set of four consecutive numbers with the same number of prime factors. 1309, 1310, and 1311 are also the smallest three consecutive numbers that have exactly the same number of factors and factor pairs. Thank you OEIS.org for alerting me to those facts.

Finally, although the list of primes is slightly out of order, here’s a fun fact related to 1311 that I saw on Twitter: