# 1602 Mystery

### Today’s Puzzle:

Is the logic needed to solve this puzzle simple or complicated? That question is part of the mystery!

### Factors of 1602:

• 1602 is a composite number.
• Prime factorization: 1602 = 2 × 3 × 3 × 89, which can be written 1602 = 2 × 3² × 89.
• 1602 has at least one exponent greater than 1 in its prime factorization so √1602 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1602 = (√9)(√178) = 3√178.
• The exponents in the prime factorization are 1, 2, and 1. Adding one to each exponent and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 1602 has exactly 12 factors.
• The factors of 1602 are outlined with their factor pair partners in the graphic below.

### More about the Number 1602:

How is 1602 the sum of two squares?
39² + 9² = 1602.

How is 1602 the hypotenuse of a Pythagorean triple?
702-1440-1602, calculated from 2(39)(9), 39² – 9², 39² + 9².
That triple is also 9 times (78-160-178).