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Which one of the following is a composite number?

Class 10Real NumbersNumber Systems
  • A
  • B23
  • C37
  • D41

Step-by-Step Solution

, which has a factor 13 (and 78), so it is composite. The others (23, 37, 41) are prime.
Answer: A)

Key idea: Fundamental Theorem of Arithmetic

**Theorem**: Every composite number can be expressed as a product of primes — UNIQUELY, up to the order of factors.

Example: . There is no other set of primes whose product is 360.

**Consequences**:
1. **Finding HCF** by primes: HCF = product of LOWEST powers of common primes.
2. **Finding LCM** by primes: LCM = product of HIGHEST powers of all primes appearing.
3. **Identity**: HCF(a,b) × LCM(a,b) = .

Example: . HCF = 2·3 = 6, LCM = . Check: . ✓

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