Vidaara.orgClass 10 · Mathematics
CodeVID-M10-01-EDL-01
Euclid’s Division Lemma — Assignment
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.
Euclid's lemma: $a=bq+r$ with:
- A.$0\le r
- B.$0
- C.$r=0$
- D.$r>b$
- B.$0
2.
The HCF of $6$ and $8$ is:
- A.$1$
- B.$2$
- C.$4$
- D.$24$
3.
HCF$(18,24)=$
- A.$3$
- B.$6$
- C.$12$
- D.$2$
4.
The HCF of two coprime numbers is:
- A.$0$
- B.$1$
- C.$2$
- D.their LCM
5.
HCF$(0,5)=$
- A.$0$
- B.$5$
- C.$1$
- D.undefined
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the HCF of $12$ and $18$.
7.
Write $17=5q+r$ using Euclid's lemma.
8.
Find HCF$(36,84)$.
9.
Are $8$ and $15$ coprime?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find HCF$(135,225)$ using Euclid's algorithm.
11.
Find HCF$(196,38220)$.
12.
Show that any positive odd integer is of the form $4q+1$ or $4q+3$.
13.
Find the largest number dividing $70$ and $125$ leaving remainders $5$ and $8$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the HCF of $867$ and $255$ using Euclid's division algorithm.
15.
Find the largest number which divides $2053$ and $967$ leaving remainders $5$ and $7$ respectively.
Answer Key
Section A — Multiple Choice Questions
- (A) $0\le r
- (B) $2$
- (B) $6$
- (B) $1$
- (B) $5$
Section B — Short Answer (2 marks)
- $6$.
- $17=5\cdot3+2$.
- $12$.
- Yes.
Section C — Short Answer (3 marks)
- $45$.
- $196$.
- Established (odd integers leave remainder $1$ or $3$ on division by $4$).
- $13$.
Section D — Long Answer (5 marks)
- $51$.
- $64$.
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