# 263 How and Why You Should Show Your Work

• 263 is a prime number.
• Prime factorization: 263 is prime.
• The exponent of prime number 263 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 263 has exactly 2 factors.
• Factors of 263: 1, 263
• Factor pairs: 263 = 1 x 263
• 263 has no square factors that allow its square root to be simplified. √263 ≈ 16.217

How do we know that 263 is a prime number? If 263 were not a prime number, then it would be divisible by at least one prime number less than or equal to √263 ≈ 16.217. Since 263 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 263 is a prime number.

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Joseph Nebus reads hundreds of comics every day as he looks for ones with a mathematical theme. He regularly shares these finds on his blog and writes a short explanation about the mathematics mentioned in the comics. I especially loved his reading-the-comics-october-14-2014 edition.

Why mathematics students should show their work is clearly explained under Jeff Mallet’s Frazz (October 12) comic strip.  Joseph Nebus basically gives two reasons to show work. The first reason has probably been stated by teachers thousands of times, but the second is truly an inspiration, and I highly recommend teachers and students alike read it!

How should the work be shown? This You-tube video does a very good job showing how to show work and make that work as readable as possible.