# 1183 is the 13th Pentagonal Pyramidal Number

1183 is the 13th pentagonal pyramidal number. Here’s an attempt to illustrate that fact. (Try to think 3-dimensionally.):

Here are some more facts about the number 1183:

• 1183 is a composite number.
• Prime factorization: 1183 = 7 × 13 × 13, which can be written 1183 = 7 × 13²
• The exponents in the prime factorization are 1 and 2. Adding one to each and multiplying we get (1 + 1)(2 + 1) = 2 × 3  = 6. Therefore 1183 has exactly 6 factors.
• Factors of 1183: 1, 7, 13, 91, 169, 1183
• Factor pairs: 1183 = 1 × 1183, 7 × 169, or 13 × 91
• Taking the factor pair with the largest square number factor, we get √1183 = (√169)(√7) = 13√7 ≈ 34.39476

1183 is the hypotenuse of two Pythagorean triples:
833-840-1183 which is 7 times (119-120-169)
455-1092-1183 which is (5-12-13) times 91

I like 1183 in a couple of different bases:
It’s palindrome 1121211 in BASE 3 because
3⁶ + 3⁵ + 2(3⁴) + 3³ + 2(3²) + 3 + 1 = 1183,
and it’s 700 in BASE 13 because 7(13²) = 1183