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The reason 1135 is a centered triangular number is illustrated in this graphic:
(26×27 + 27×28 + 28×29)/2 = 1135 means that 1135 is the sum of the 26th, 27th, and 28th triangular numbers. The sum of three consecutive triangular numbers is always a centered triangular number.
Here are some more facts about the number 1135:
- 1135 is a composite number.
- Prime factorization: 1135 = 5 × 227
- 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 1135 has exactly 4 factors.
- Factors of 1135: 1, 5, 227, 1135
- Factor pairs: 1135 = 1 × 1135 or 5 × 227
- 1135 has no square factors that allow its square root to be simplified. √1135 ≈ 33.68976
1135 is the sum of the seventeen prime numbers from 31 to 103.
It is also the sum of three consecutive prime numbers:
373 + 379 + 383 = 1135
1135 is the hypotenuse of a Pythagorean triple:
681-908-1135 which is (3-4-5) times 227
1135 is a palindrome in two different bases:
It’s 7A7 in BASE 12 (A is 10 base 10) because 7(12²) + 10(12) + 7(1) = 1135,
and 1F1 in BASE 27 (F is 15 Base 10) because 27² + 15(27) + 1 = 1135