The shepherds’ crooks from that first Christmas night have become the sweet candy canes we often see on today’s Christmas trees. Can you find the factors from 1 to 12 that will make this mystery level puzzle function like a multiplication table? Remember to use logic to find the factors.
Factors of 1571:
1571 is a prime number.
Prime factorization: 1571 is prime.
1571 has no exponents greater than 1 in its prime factorization, so √1571 cannot be simplified.
The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1571 has exactly 2 factors.
The factors of 1571 are outlined with their factor pair partners in the graphic below.
How do we know that 1571 is a prime number? If 1571 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1571. Since 1571 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, or 37, we know that 1571 is a prime number.
More about the Number 1571:
1571 is the sum of two consecutive numbers:
785 + 786 = 1571.
1571 is also the difference of two squares:
786² – 785² = 1571.
Do you see the relationship between those two facts?
Candy canes are rarely alone. They almost always have a twin close-by. Nevertheless, this mystery-level candy cane puzzle only looks similar to the previous one. You will have to consider completely different factors to solve it.
Candy canes have been a part of the Christmas season for ages. Here’s a candy cane puzzle for you to try. It’s a level 6 so it won’t be easy, but you will taste its sweetness once you complete it. Go ahead and get started!
983 is the sum of consecutive prime numbers two different ways:
It is the sum of the seventeen prime numbers from 23 to 97.
It is also the sum of the thirteen prime numbers from 47 to 103.
983 is a prime number.
Prime factorization: 983 is prime.
The exponent of prime number 983 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 983 has exactly 2 factors.
Factors of 983: 1, 983
Factor pairs: 983 = 1 × 983
983 has no square factors that allow its square root to be simplified. √983 ≈ 31.35283
How do we know that 983 is a prime number? If 983 were not a prime number, then it would be divisible by at least one prime number less than or equal to √983 ≈ 31.4. Since 983 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 983 is a prime number.