A few weeks ago Brilliant Quotes tweeted a quote from Duke Ellington: “A problem is a chance for you to do your best.”

I immediately thought of problems students are given in mathematics classes because this quote applies to those problems.

It also applies to any other kind of problem a person may face. Sometimes those problems are much more challenging than problems involving numbers. All problems are opportunities for us to do our best.

Let’s find the factoring information for a relatively easy number – 393.

• 393 is a composite number.
• Prime factorization: 393 = 3 x 131
• 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 393 has exactly 4 factors.
• Factors of 393: 1, 3, 131, 393
• Factor pairs: 393 = 1 x 393 or 3 x 131
• 393 has no square factors that allow its square root to be simplified. √393 ≈ 19.824

Is 393 in any Pythagorean triples?

• 393-524-655  which is [3 – 4 – 5] times 131
• 393-25740-25743 which is [131-8580-8581] times 3
• Primitive 393-8576-8585
• and Primitive 393-77224-77225

At the end of his post a-promise-broken, Established1962 tells a personal and very funny story involving his copy of Duke Ellington’s autobiography, “Music Is My Mistress.” The quote above is included in that book.