Question

Find the HCF of 405, 585, 765 and 900.

• A. \(35\)
• B. \(45\)
• C. \(55\)
• D. \(65\)
• E. \(25\)

Answer 1

The Correct Option is B

Concept: HCF (Highest Common Factor) is the greatest number that divides all given numbers. It can be found using prime factorization.
Step 1: Prime factorization.
\[ 405 = 3^4 \times 5 \] \[ 585 = 3^2 \times 5 \times 13 \] \[ 765 = 3^2 \times 5 \times 17 \] \[ 900 = 2^2 \times 3^2 \times 5^2 \]
Step 2: Take common factors with lowest powers.
Common primes: \[ 3^2 \text{ and } 5 \]
Step 3: Compute HCF.
\[ \text{HCF} = 3^2 \times 5 = 9 \times 5 = 45 \]
Step 4: Option analysis.

• (A) 35: Not common factor $\times$
• (B) 45: Correct \checkmark
• (C) 55: Not common $\times$
• (D) 65: Not common $\times$
• (E) 25: Missing factor 3 $\times$

Conclusion:
Thus, the correct answer is
Option (B).