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Mathematics — CBSE Class 10 board question

Q1. [1]
The HCF of 40, 110 and 360 is :
  1. A $40$
  2. B $110$
  3. C $360$
  4. D $10$
Previously asked in CBSE board exam
2025 30/2/1 Q18
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer

Option D: 10

$40 = 2^3 \times 5,\ 110 = 2 \times 5 \times 11,\ 360 = 2^3 \times 3^2 \times 5$. HCF = product of smallest powers of common prime factors = $2^1 \times 5^1 = \mathbf{10}$.

Source: Chapter 1, Section 1.2 (Fundamental Theorem of Arithmetic)

Explanation

HCF is found by taking the lowest power of each prime factor common to all three numbers. Here, 2 and 5 are common to all three; their minimum powers are $2^1$ and $5^1$, giving HCF = 10. Note that 40 divides only 40 and 360 (not 110), so option A is wrong. Always check all three numbers share the factor.

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