# 823 and Level 2

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.

## 2 thoughts on “823 and Level 2”

1. Charles Sanders

This is so interesting. I have been trying to figure this out

• ivasallay

Welcome! I’m sure you will figure it out!

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