1459 and Level 4

Today’s Puzzle:

Can you place the numbers 1 to 10 in both the first column and the top row so that those numbers are the factors of the given clues? You might surprise yourself with how well you do!

Factors of 1459:

  • 1459 is a prime number.
  • Prime factorization: 1459 is prime.
  • 1459 has no exponents greater than 1 in its prime factorization, so √1459 cannot be simplified.
  • The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1459 has exactly 2 factors.
  • The factors of 1459 are outlined with their factor pair partners in the graphic below.

How do we know that 1459 is a prime number? If 1459 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1459. Since 1459 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 31, or 37, we know that 1459 is a prime number.

Other Facts about the number 1459:

1459 is the difference of two squares:
730² – 729² = 1459

From Stetson.edu we learn this chilling cubic fact:
1³ + 4³ + 5³ + 9³ = 919, and
9³ + 1³ + 9³ = 1459

 

Advertisements