# 1289 and Level 1

You might think this is a very easy puzzle, but for some people, it will be challenging, and will hopefully help them learn some multiplication facts better. Print the puzzles or type the solution in this excel file: 12 factors 1289-1299

Since this is puzzle number 1289, I’ll share some facts about that number:

• 1289 is a prime number.
• Prime factorization: 1289 is prime.
• The exponent of prime number 1289 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1289 has exactly 2 factors.
• Factors of 1289: 1, 1289
• Factor pairs: 1289 = 1 × 1289
• 1289 has no square factors that allow its square root to be simplified. √1289 ≈ 35.90265

How do we know that 1289 is a prime number? If 1289 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1289 ≈ 35.9. Since 1289 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1289 is a prime number. 1289 is the sum of two squares:
35² + 8² = 1289

1289 is the hypotenuse of a Pythagorean triple:
560-1161-1289 calculated from 2(35)(8), 35² – 8², 35² + 8²

Here’s another way we know that 1289 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 35² + 8² = 1289 with 35 and 8 having no common prime factors, 1289 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1289 ≈ 35.9. Since 1289 is not divisible by 5, 13, 17, or 29, we know that 1289 is a prime number.

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