# 1388 Mystery Level

Sometimes puzzles start out easy enough but get a little more complicated later on. Does that happen with this puzzle? There’s only one way to find out! Print the puzzles or type the solution in this excel file: 10 Factors 1373-1388

Here are some facts about the number 1388:

• 1388 is a composite number.
• Prime factorization: 1388 = 2 × 2 × 347, which can be written 1388 = 2² × 347
• 1388 has at least one exponent greater than 1 in its prime factorization so √1388 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1388 = (√4)(√347) = 2√347
• The exponents in the prime factorization are 2 and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1) = 3 × 2 = 6. Therefore 1388 has exactly 6 factors.
• The factors of 1388 are outlined with their factor pair partners in the graphic below. 1388 is the difference of two squares:
348² – 346² = 1388

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