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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-01-FTA-01
Fundamental Theorem of Arithmetic — Assignment
Chapter: Number Systems
Topic: Fundamental Theorem of Arithmetic
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Every composite number is a product of primes:
  • A.in many ways
  • B.uniquely
  • C.never
  • D.only if even
2.
The prime factorisation of $60$ is:
  • A.$2^2\cdot3\cdot5$
  • B.$2\cdot30$
  • C.$4\cdot15$
  • D.$2^3\cdot5$
3.
HCF$\times$LCM $=$
  • A.$a+b$
  • B.$a\cdot b$
  • C.$a-b$
  • D.$1$
4.
LCM$(6,8)=$
  • A.$2$
  • B.$24$
  • C.$48$
  • D.$14$
5.
The number $1$ is:
  • A.prime
  • B.composite
  • C.neither prime nor composite
  • D.even
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Write the prime factorisation of $84$.
7.
Find LCM$(12,15)$.
8.
Find HCF$\times$LCM for $12$ and $18$.
9.
Find HCF$(12,18)$ by prime factorisation.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the HCF and LCM of $96$ and $404$.
11.
Find the HCF and LCM of $6,72,120$.
12.
If HCF$(a,b)=9$, LCM$=90$ and $a=18$, find $b$.
13.
Can $6^n$ end with the digit $0$ for any natural $n$?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the HCF and LCM of $510$ and $92$ and verify HCF$\times$LCM $=$ product.
15.
Explain why $7\times11\times13+13$ is a composite number.

Answer Key

Section A — Multiple Choice Questions
  1. (B) uniquely
  2. (A) $2^2\cdot3\cdot5$
  3. (B) $a\cdot b$
  4. (B) $24$
  5. (C) neither prime nor composite
Section B — Short Answer (2 marks)
  1. $2^2\cdot3\cdot7$.
  2. $60$.
  3. $216$.
  4. $6$.
Section C — Short Answer (3 marks)
  1. HCF $4$, LCM $9696$.
  2. HCF $6$, LCM $360$.
  3. $45$.
  4. No (it has no factor $5$).
Section D — Long Answer (5 marks)
  1. HCF $2$, LCM $23460$ (verified).
  2. $=13(7\times11+1)=13\times78$, so it has factors — composite.
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