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Two factors of 1247 make it the 29th pentagonal number. Here’s why:
29(3·29-1)/2 = 29(86)/2 = 29(43) = 1247
Here is an illustration of this pentagonal number featuring a different, but equivalent, formula. Seeing the pentagonal numbers less than 1247 in the illustration won’t be difficult either.
Here are some more facts about the number 1247:
- 1247 is a composite number.
- Prime factorization: 1247 = 29 × 43
- 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 1247 has exactly 4 factors.
- Factors of 1247: 1, 29, 43, 1247
- Factor pairs: 1247 = 1 × 1247 or 29 × 43
- 1247 has no square factors that allow its square root to be simplified. √1247 ≈ 35.31289
1247 is the sum of consecutive prime numbers two different ways:
It is the sum of the twenty-three prime numbers from 11 to 103.
It is also the sum of seven consecutive primes:
163 + 167 + 173 + 179 + 181 + 191 + 193 = 1247
1247 is the hypotenuse of a Pythagorean triple:
860-903-1247 which is (20-21-29) times 43