## A Multiplication Based Logic Puzzle

### 694 and Level 6

• 694 is a composite number.
• Prime factorization: 694 = 2 x 347
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 694 has exactly 4 factors.
• Factors of 694: 1, 2, 347, 694
• Factor pairs: 694 = 1 x 694 or 2 x 347
• 694 has no square factors that allow its square root to be simplified. √694 ≈ 26.34388.

Level 6 puzzles aren’t easy, but do give it a try! There are hints at the bottom of the page.

Print the puzzles or type the solution on this excel file: 10 Factors 2015-11-23

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Here are some ways that 694 is a special number:

694 is the 22nd centered triangular number because it is the sum of these consecutive triangular numbers 210, 231, 253.

Notice that 21(22)/2 is 231, the number in the middle of those consecutive triangular numbers. Also notice that 3(231) + 1 = 694.

694 BASE 10 becomes palindrome 1C1 in BASE 21 because C Base 21 is equivalent to 12 Base 10, and 1(21²) + 12(21) + 1(1) = 694.

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