Today’s Puzzle:

Can you find the factors for this mystery-level puzzle? There is only one solution.

Factors of 1783:

• 1783 is a prime number.
• Prime factorization: 1783 is prime.
• 1783 has no exponents greater than 1 in its prime factorization, so √1783 cannot be simplified.
• The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1783 has exactly 2 factors.
• The factors of 1783 are outlined with their factor pair partners in the graphic below.

How do we know that 1783 is a prime number? If 1783 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1783. Since 1783 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, or 41, we know that 1783 is a prime number.

More About the Number 1783:

1783 is palindrome 1L1 in base 33 because
1(33²) + 21(33) + 1(1) = 1783.

1783 is the sum of two consecutive numbers:
891 + 892 = 1783.

1783 is the difference of the squares of those same two consecutive numbers:
892² – 891² = 1783.
Of course, every other odd number can make a similar claim.