# 776 and Level 3

• 776 is a composite number.
• Prime factorization: 776 = 2 x 2 x 2 x 97, which can be written 776 = (2^3) x 97
• The exponents in the prime factorization are 3 and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 x 2 = 8. Therefore 776 has exactly 8 factors.
• Factors of 776: 1, 2, 4, 8, 97, 194, 388, 776
• Factor pairs: 776 = 1 x 776, 2 x 388, 4 x 194, or 8 x 97
• Taking the factor pair with the largest square number factor, we get √776 = (√4)(√194) = 2√194 ≈ 27.85677655 Try solving today’s puzzle: Print the puzzles or type the solution on this excel file: 10-factors-2016

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Here’s more about the number 776:

776 is the sum of two squares: 26² + 10² =776.

776 is the hypotenuse of Pythagorean triple 520-576-776 so 520² + 576² = 776².

776 is also the sum of three squares five different ways:

• 26² + 8² + 6² = 776
• 24² + 14² + 2² = 776
• 24² + 10² + 10² = 776
• 22² + 16² + 6² = 776
• 18² + 16² + 14² = 776

776 is a palindrome in three other bases:

• 646 BASE 11; note that 6(121) + 4(11) + 6(1) = 776
• 272 BASE 18; note that 2(18²) + 7(18) + 2(1) = 776
• 161 BASE 25; note that 1(25²) + 6(25) + 1(1) = 776

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