Fundamental Theorem of Arithmetic
Unique factorisation into primes.
Key idea
Unique factorisation into primes.
In depth
Every integer greater than 1 factors into primes, uniquely up to order. Uniqueness is a key property: it fails in some other number systems.
Worked example
360 = 2³ × 3² × 5, and no other prime factorisation exists.
Real-world uses
- Understanding unique prime building blocks used in cryptography and simplifying fractions
Common mistake
Assuming unique factorisation holds in every number system.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Fundamental Theorem of Arithmetic?
Unique factorisation into primes. It is a topic at the advanced level in Discrete Math & Number Theory.
Where is Fundamental Theorem of Arithmetic used in real life?
Real-world examples: Understanding unique prime building blocks used in cryptography and simplifying fractions.
What should I learn before Fundamental Theorem of Arithmetic?
Make sure you are comfortable with Division Algorithm, the previous topic in Discrete Math & Number Theory.
What is a common mistake with Fundamental Theorem of Arithmetic?
Assuming unique factorisation holds in every number system.
How can I practise Fundamental Theorem of Arithmetic?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Fundamental Theorem of Arithmetic?
Move on to Infinitude of Primes next.
Related advanced topics in Discrete Math & Number Theory
- Tautologies and Contradictions – Always true or always false statements.
- Logical Equivalence – Statements with identical truth tables.
- De Morgan’s Laws – Negation swaps AND and OR.
- Converse and Contrapositive – A conditional equals its contrapositive.
- Quantifiers – “For all” and “there exists”.
- Negating Quantified Statements – Flip the quantifier and negate the predicate.