# 888 and Level 2

888 consists of three 8’s, so it is divisible by 3. Print the puzzles or type the solution on this excel file: 12 factors 886-896

888 is the hypotenuse of a Pythagorean triple:

• 288-840-888 which is 24 times (12-35-37)

888 is the sum of eight consecutive prime numbers:

• 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 = 888

888 is a palindrome in BASE 15 and a repdigit in BASE 36:

• 3E3 BASE 15 (E is 14 in base 10), because 3(15²) + 14(15) + 3(1) = 888
• OO BASE 36 (O is 24 in base 10), because 24(26) + 24(1) = 24(27) = 888

How many factors does 888 have?

• 888 is a composite number.
• Prime factorization: 888 = 2 × 2 × 2 × 3 × 37, which can be written 888 = 2³ × 3 × 37
• The exponents in the prime factorization are 3, 1, and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1)(1 + 1) = 4 × 2 × 2 = 16. Therefore 888 has exactly 16 factors.
• Factors of 888: 1, 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, 444, 888
• Factor pairs: 888 = 1 × 888, 2 × 444, 3 × 296, 4 × 222, 6 × 148, 8 × 111, 12 × 74, or 24 × 37
• Taking the factor pair with the largest square number factor, we get √888 = (√4)(√222) = 2√222 ≈ 29.7993. 