- 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.

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.

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