Beautiful shamrocks with their three heart-shaped leaves are not difficult to find. Finding the factors in this shamrock-shaped puzzle might be a different story. Sure, it might start off to be easy, but after a while, you might find it a wee bit more difficult, unless, of course, the luck of the Irish is with you!

Print the puzzles or type the solution in this excel file: 12 Factors 1357-1365

Now I’ll share some information about the number 1365:

- 1365 is a composite number.
- Prime factorization: 1365 = 3 × 5 × 7 × 13
- The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 × 2 = 16. Therefore 1365 has exactly 16 factors.
- Factors of 1365: 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365
- Factor pairs: 1365 = 1 × 1365, 3 × 455, 5 × 273, 7 × 195, 13 × 105, 15 × 91, 21 × 65, or 35 × 39
- 1365 has no square factors that allow its square root to be simplified. √1365 ≈ 36.94591

1365 is the hypotenuse of FOUR Pythagorean triples:

336-1323-1365 which is **21** times (16-63-**65**)

525-1260-1365 which is (5-12-**13**) times **105**

693-1176-1365 which is **21** times (33-56-**65**)

819-1092-1365 which is (3-4-**5**) times **273**

1365 looks interesting in some other bases:

It’s 10101010101 in BASE 2,

111111 in BASE 4,

2525 in BASE 8, and

555 in BASE 16

I’m feeling pretty lucky that I noticed all those fabulous number facts! If you haven’t been so lucky finding the factors of the puzzle, the same puzzle but with more clues might help: