Today’s Puzzle:

Mother’s Day in the United States is this Sunday so I made this challenging flower puzzle for the occasion.

Use logic to write the numbers from 1 to 10 in each of the four boldly outlined areas so that those numbers and the given clues work together to make four multiplication tables.

Factors of 1637:

• 1637 is a prime number.
• Prime factorization: 1637 is prime.
• 1637 has no exponents greater than 1 in its prime factorization, so √1637 cannot be simplified.
• The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1637 has exactly 2 factors.
• The factors of 1637 are outlined with their factor pair partners in the graphic below.

How do we know that 1637 is a prime number? If 1637 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1637. Since 1637 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, or 37, we know that 1637 is a prime number.

More about the Number 1637:

1637 is the sum of two squares:
31² + 26² = 1637.

1637 is the hypotenuse of a Pythagorean triple:
285-1612-1637, calculated from 31² – 26², 2(31)(26), 31² + 26².

Here’s another way we know that 1637 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 31² + 26² = 1637 with 31 and 26 having no common prime factors, 1637 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1637. Since 1637 is not divisible by 5, 13, 17, 29, or 37, we know that 1637 is a prime number.

Do you notice anything else special about the number 1637 in this color-coded chart?