Highest Common Factor (HCF)

PART-B Unit I: Aptitude

PART-B • Unit I: Aptitude & Mental Ability

Highest Common Factor (HCF / GCD) • 15 Model Questions

Organized from Easy to Complex with Step-by-Step Mathematical Solutions and LaTeX Formulas

Level 1: Integer & Monomial Algebraic HCF

Easy
Question 01 Two-Integer HCF (Euclidean / Factorization)
Find the Highest Common Factor (HCF) of \(408\) and \(170\):
(A) \(36\)
(B) \(34\)  ✓
(C) \(33\)
(D) \(30\)
💡 Explanation:
  • Prime Factorization: \[408 = 2^3 \times 3 \times 17\] \[170 = 2 \times 5 \times 17\]
  • HCF: Product of the lowest powers of common prime factors: \[\mathrm{HCF}(408, 170) = 2^1 \times 17^1 = \mathbf{34}\]
  • Euclidean Division Method: \(408 = 170 \times 2 + 68 \implies 170 = 68 \times 2 + 34 \implies 68 = 34 \times 2 + 0\). Thus, \(\mathrm{HCF} = 34\).
Correct Option: (B) 34
Highest Common Factor (HCF)”.

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