Today I’m saying “Happy Birthday” to my son, Brent with a yummy but mysterious puzzle cake. I’ve made the puzzle just a little bit harder than normal.

Adding 13 to the puzzle actually makes it easier to solve, but adding 14 makes some multiples of 7 more difficult. For example, the allowable common factors of 70 and 35 are now 7 AND 5, and the allowable common factors of 28 and 56 are now 4, 7, and 14.

As always there is only one solution. I know my son can solve this puzzle, Can you?

Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Now I’ll share some facts about the number 1191:

• 1191 is a composite number.
• Prime factorization: 1191 = 3 × 397
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1191 has exactly 4 factors.
• Factors of 1191: 1, 3, 397, 1191
• Factor pairs: 1191 = 1 × 1191 or 3 × 397
• 1191 has no square factors that allow its square root to be simplified. √1191 ≈ 34.51087

1191 is the hypotenuse of a Pythagorean triple:
684-975-1191 which is 3 times (228-325-397)

1191 is repdigit 111 in BASE 34 because
34² + 34 + 1 = 35(34) + 1 = 1191