# 1272 and Level 2

Some of the factor pairs needed to solve this puzzle may be easier for you to find than others, but I’m sure you can still find all of them. Give it a try! Print the puzzles or type the solution in this excel file: 12 factors 1271-1280

Now I’ll write a little bit about the number 1272:

• 1272 is a composite number.
• Prime factorization: 1272 = 2 × 2 × 2 × 3 × 53, which can be written 1272 = 2³ × 3 × 53
• 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 1272 has exactly 16 factors.
• Factors of 1272: 1, 2, 3, 4, 6, 8, 12, 24, 53, 106, 159, 212, 318, 424, 636, 1272
• Factor pairs: 1272 = 1 × 1272, 2 × 636, 3 × 424, 4 × 318, 6 × 212, 8 × 159, 12 × 106, or 24 × 53
• Taking the factor pair with the largest square number factor, we get √1272 = (√4)(√318) = 2√318 ≈ 35.66511 1272 is the sum of four consecutive prime numbers, and it is the sum of two consecutive prime numbers:
311 + 313 + 317 + 331 = 1272
631 + 641 = 1272

1272 is the hypotenuse of a Pythagorean triple:
672-1080-1272 which is 24 times (28-45-52)

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