# 1099 and Level 5

The allowable common factors fro 8 and 24 are 2, 4, and 8. Which one of those should you choose? Find a different place to start the puzzle and you shouldn’t have to guess and check to see if you were right. Print the puzzles or type the solution in this excel file: 12 factors 1095-1101

Here are some facts about the number 1099:

• 1099 is a composite number.
• Prime factorization: 1099 = 7 × 157
• 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 1099 has exactly 4 factors.
• Factors of 1099: 1, 7, 157, 1099
• Factor pairs: 1099 = 1 × 1099 or 7 × 157
• 1099 has no square factors that allow its square root to be simplified. √1099 ≈ 33.15117 1099 = 1 + 0 + 999 + 99. Thank you OEIS.org for that fun fact.

1099 is the sum of the 13 prime numbers from 59 to 109.
That’s a fact that would take little effort to memorize!

1099 is also the sum of these prime numbers:
139 + 149 +  151 + 157 + 163 + 167 + 173 = 1099
359 + 367 + 373 = 1099

1099 is the hypotenuse of a Pythagorean triple:
595-924-1099 which is 7 times (85-132-157)

1099 is repdigit 777 in BASE 12 because 7(12² + 12 + 1) = 7(157) = 1099
1099 is palindrome 4D4 in BASE 15 (D is 13 in base 10)
because 4(15²) + 13(15) + 4(1) = 1099

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