274

274 and Level 6

/ ivasallay / 2 Comments

  • 274 is a composite number.
  • Prime factorization: 274 = 2 x 137
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 274 has 4 factors.
  • Factors of 274: 1, 2, 137, 274
  • Factor pairs: 274 = 1 x 274 or 2 x 137
  • 274 has no square factors that allow its square root to be simplified. √274 ≈ 16.553.

I recommend using logic and not guess and check to solve the Find the Factors puzzles, but the logic for the one below can be a little tricky. If necessary, scroll down for one piece of reasoning that may be helpful if you get stuck in the middle of trying to solve this one.

2014-42 Level 6

 Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-20

Notes on some logic needed for this puzzle:

  • The choices for 24 are 2 x 12, 3 x 8, or 4 x 6.
  • Because 28 = 4 x 7, 16 = 2 x 8, not 4 x 4. Thus 16 will use one of the 2’s. Either 6 or 8 will use the other 2, so we eliminate  2 x 12 = 24.
  • Also 21 will use one of the 3’s while 6 or 18 will use the other. Thus we eliminate  3 x 8 = 24.
  • Therefore 24 = 4 x 6 or 6 x 4.

2014-42 Level 6 Logic