1567 Peppermint Stick

Today’s Puzzle:

Our mystery level puzzle looks like a sweet stick of Christmas candy. Will solving it be sweet or will it be sticky? You’ll have to try it yourself to know.

Factors of 1567:

  • 1567 is a prime number.
  • Prime factorization: 1567 is prime.
  • 1567 has no exponents greater than 1 in its prime factorization, so √1567 cannot be simplified.
  • The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1567 has exactly 2 factors.
  • The factors of 1567 are outlined with their factor pair partners in the graphic below.

How do we know that 1567 is a prime number? If 1567 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1567. Since 1567 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, or 37, we know that 1567 is a prime number.

More about the Number 1567:

1567 is the sum of two consecutive numbers:
783 + 784 = 1567.

1567 is also the difference of two consecutive squares:
784² – 783² = 1567.

982 Red-Hot Cinnamon Candy

When I was a child I remember eating a red-hot cinnamon ball around the holidays. I really like cinnamon, but I wasn’t sure I liked how hot the candy was. I hope you enjoy today’s red-hot cinnamon candy puzzle.

Print the puzzles or type the solution in this excel file: 12 factors 978-985

Now here’s something interesting about the number 982:

It is palindrome 292 in BASE 20 because 2(20²) + 9(20) + 2(1) = 982.

  • 982 is a composite number.
  • Prime factorization: 982 = 2 × 491
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 982 has exactly 4 factors.
  • Factors of 982: 1, 2, 491, 982
  • Factor pairs: 982 = 1 × 982 or 2 × 491
  • 982 has no square factors that allow its square root to be simplified. √982 ≈ 31.336879