# 1567 Peppermint Stick

Contents

### 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.

This site uses Akismet to reduce spam. Learn how your comment data is processed.