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Which of these numbers CANNOT be written as a product of two DISTINCT prime numbers?

Class 10Real NumbersNumber Systems
  • A35
  • B51
  • C49
  • D91

Step-by-Step Solution

35 = and are each a product of two different primes. But uses the same prime twice, so its two prime factors are not distinct. Assuming 51 and 91 are prime (they are not) is the usual trap here.
Answer: C) 49

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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