📚 CBSE Grade-10 Study Guide Open in the Study Guide single page app →
HomeMathematics

Mathematics — CBSE Class 10 board question

Q1. [1]
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.

If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to Library and find the actual CBSE question paper. The original papers are also available on the CBSE website: cbse.gov.in.
Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.