Problem of the Week #93: Monday June 23rd, 2025
As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems.
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a). If we were to extend the definition of factors to non-integers, which of the following would you say is a factor of 2/5: 2? 5? 1/5? 1/10? 2/15?
b). What’s the GCF of 2/5 and 3/7? LCM?
c). Is there an equivalent of prime numbers when we talk about factors of fractions? Give examples or explain why not.
d). Does the formula GCF(a, b) x LCM(a,b) = axb still work when a and b are fractions? What about the Euclidean Algorithm?
e). Can two irrational numbers have common factors? Common multiples?
f). Can a rational number and an irrational number have common factors? Common multiples?
g). Share your own problem inspired by this one.
h). Give one of these questions to a friend/colleague/student/family member to start a mathematical discussion.
Also check out the video I made on this topic.