# 1352 and Level 3

If you know what numbers divide evenly into both 3 and 15, then you can solve this puzzle. Only use factor pairs where both numbers are from 1 to 10. Start at the top of the puzzle and work down cell by cell until you have found all the factors! Print the puzzles or type the solution in this excel file: 10 Factors 1347-1356

Here I explain how to solve the above puzzle:

Here are a few facts about the puzzle number, 1352:

• 1352 is a composite number.
• Prime factorization: 1352 = 2 × 2 × 2 × 11 × 11, which can be written 1352 = 2³ × 13²
• 1352 has at least one exponent greater than 1 in its prime factorization so √1352 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1352 = (√676)(√2) = 26√2
• The exponents in the prime factorization are 3 and 2. Adding one to each exponent and multiplying we get (3 + 1)(2 + 1) = 4 × 3 = 12. Therefore 1352 has exactly 12 factors.
• The factors of 1352 are outlined with their factor pair partners in the graphic below. 1352 is the hypotenuse of two Pythagorean triples:
520-1248-1352 which is (5-12-13) times 104
952-960-1352 which is 8 times (119-120-169)

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