The last two digits of 4**24** can be evenly divided by 4 so **424** can also be evenly divided by 4. Also because 24 is divisible by 8 and because the digit preceding the 24 is even, **424** is also divisible by 8. All of the factors of 424 are listed below the puzzle.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-03-09

- 424 is a composite number.
- Prime factorization: 424 = 2 x 2 x 2 x 53, which can be written 424 = (2^3) x 53
- The exponents in the prime factorization are 3 and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 x 2 = 8. Therefore 424 has exactly 8 factors.
- Factors of 424: 1, 2, 4, 8, 53, 106, 212, 424
- Factor pairs: 424 = 1 x 424, 2 x 212, 4 x 106, or 8 x 53
- Taking the factor pair with the largest square number factor, we get √424 = (√4)(√106) = 2√106 ≈ 20.5913

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