Q1
Every composite number can be expressed as a product of:
Aprimes
Beven numbers
Codd numbers only
Dperfect squares only
CBSEClass 10 (CBSE)MathematicsCh 1 · Topic 2
Fundamental Theorem of Arithmetic
Learning that every composite number can be uniquely factorised into primes.
Core concept
This theorem is used to efficiently find the HCF and LCM of numbers using prime factorisation: HCF is the product of the smallest powers of common prime factors, while LCM is the product of the highest powers of all prime factors present in either number. It's also used to prove that numbers like √2 are irrational, through a proof by contradiction that relies on this theorem's guarantee of unique prime factorisation.
Exam highlight
Key diagram
Keywords worth remembering
Trending
fundamental theorem of arithmeticcbse class 10
Most searched
CBSE class 10 fundamental theorem of arithmetic
Quick revision
Study resources
Notes & downloads
Quick notes
• Fundamental Theorem of Arithmetic: every composite number is a unique product of primes.
• This uniqueness holds regardless of the order the prime factors are written in.
• Used to find HCF (smallest common prime powers) and LCM (highest prime powers) efficiently.
• Also used in proofs, like proving √2 is irrational.