All of the odd numbers between 820 and 830, except 825, are prime numbers. That makes (821, **823**, 827, 829) the fourth prime decade.

Print the puzzles or type the solution on this excel file: 10-factors-822-828

- 823 is a prime number.
- Prime factorization: 823 is prime.
- The exponent of prime number 823 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 823 has exactly 2 factors.
- Factors of 823: 1, 823
- Factor pairs: 823 = 1 x 823
- 823 has no square factors that allow its square root to be simplified. √823 ≈ 28.687977

**How do we know that ****823**** is a prime number?** If 823 were not a prime number, then it would be divisible by at least one prime number less than or equal to √823 ≈ 28.7. Since 823 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, or 23, we know that 823 is a prime number.

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