## A Multiplication Based Logic Puzzle

### 1027 Find the Factors Challenge

I’m really enjoying these Find the Factors Challenge puzzles, and I hope that you will give them a try and love them, too. You can find this one as well as a little less challenging one in the excel file link below the puzzle. You can type the factors directly on that file. Remember to use logic for every single factor pair you use.

Print the puzzles or type the solution in this excel file: 10-factors-1019-1027

Now I’ll tell you a little about the number 1027:

It is the sum of seven consecutive prime numbers:
131 + 137 + 139 + 149 + 151 + 157 + 163 = 1027

It is the sum of the squares of the first eight prime numbers:
2² +  3² +  5² +  7² +  11² +  13² +  17² +  19² = 1027
Indeed, 666 + 19² = 1027. Thanks to Stetson.edu for that fun fact.

Because 19³ – 18³ = 1027, it is the 19th Centered Hexagonal Number.
That also means that 19² + 19(18) + 18² = 1027
because a³ – b³ = (a-b)(a²+ab+b²).

1027 is the hypotenuse of a Pythagorean triple:
395-948-1027 which is (5-12-13) times 79.

1027 is also a palindrome when it is written in these three other bases:
717 in BASE 12
535 in BASE 14
1B1 in BASE 27 (B is 11 base 10)

• 1027 is a composite number.
• Prime factorization: 1027 = 13 × 79
• 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 1027 has exactly 4 factors.
• Factors of 1027: 1, 13, 79, 1027
• Factor pairs: 1027 = 1 × 1027 or 13 × 79
• 1027 has no square factors that allow its square root to be simplified. √1027 ≈ 32.0468