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Today’s Puzzle:
Solving this candy cane puzzle can be a sweet experience. Just use logic to write the numbers 1 to 12 in both the first column and the top row so that those numbers and the given clues make a multiplication table.
Factors of 1699:
- 1699 is a prime number.
- Prime factorization: 1699 is prime.
- 1699 has no exponents greater than 1 in its prime factorization, so √1699 cannot be simplified.
- The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1699 has exactly 2 factors.
- The factors of 1699 are outlined with their factor pair partners in the graphic below.
How do we know that 1699 is a prime number? If 1699 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1699. Since 1699 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, or 41, we know that 1699 is a prime number.
More About the Number 1699:
1699 is the third prime in a prime triple. What are the other two primes in that triple?
1699 is the difference of two squares:
850² – 849² = 1699.