### Today’s Puzzle:

Many of the clues in this puzzle do not appear in a 1 to 10 puzzle or a 1 to 12 puzzle. Can you find all the factors anyway? Solving this puzzle can help you solve any other Find the Factors 1 -14 puzzles.

### Factors of 1605:

- 1605 is a composite number.
- Prime factorization: 1605 = 3 × 5 × 107.
- 1605 has no exponents greater than 1 in its prime factorization, so √1605 cannot be simplified.
- The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1605 has exactly 8 factors.
- The factors of 1605 are outlined with their factor pair partners in the graphic below.

### More about the Number 1605:

1605 is the hypotenuse of a Pythagorean triple:

963-1284-1605, which is (3-4-**5**) times **321**.

1605 is the difference of two squares four different ways:

803² – 802² = 1605,

269² – 266² = 1605,

163² – 158² = 1605, and

61² – 46² = 1605.