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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [1] § 1.2 The Fundamental Theorem of Arithmetic § 1.4 Summary
The sum of the exponents of prime factors in the prime factorisation of 4004 is :
  1. A $5$
  2. B $4$
  3. C $3$
  4. D $2$
Previously asked in CBSE board exam
2025 30/2/1 Q10
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer

Option A: 5

$4004 = 2^2 \times 7 \times 11 \times 13$

Sum of exponents = 2 + 1 + 1 + 1 = 5

Source: The Fundamental Theorem of Arithmetic, Chapter 1

Explanation

Prime factorise 4004: 4004 ÷ 2 = 2002, ÷ 2 = 1001, ÷ 7 = 143, ÷ 11 = 13. So 4004 = 2² × 7¹ × 11¹ × 13¹. Add all exponents: 2+1+1+1 = 5. Students often forget to count repeated prime factors correctly — note that 2 appears twice, giving exponent 2, not 1.

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