Free · Class 10 · 6 worksheets · answer keys · practise online · set 54
Real numbers worksheets — Class 10, with answers
Free real numbers Class 10 worksheets (Chapter 1): prime factorisation, HCF and LCM, Euclid’s division algorithm, HCF × LCM, terminating decimals and irrational numbers — with answers.
💡 Learn it first
Fundamental theorem of arithmetic : every composite number is a product of primes in exactly one way: 360 = 2³ × 3² × 5.HCF = product of the smallest powers of common primes; LCM = product of the greatest powers of all primes. For two numbers, HCF × LCM = product of the numbers .Euclid’s division : a = bq + r. Keep dividing the divisor by the remainder; the last non-zero remainder is the HCF.p/q (lowest terms) has a terminating decimal only if q = 2ᵐ × 5ⁿ. √2, √3, √5, 3 + √2 are irrational ; √16 = 4 is rational.
Prime factorisation (Class 10) HCF and LCM (Class 10) Euclid’s division algorithm (Class 10) HCF × LCM = product (Class 10) Terminating decimals (Class 10) Rational or irrational? (Class 9–10)
Prime factorisation Class 10 · Worksheet 1 · set 54
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1150 Prime factorisation of 244 Prime factorisation of 1388 Prime factorisation of 2166 Prime factorisation of 812 Prime factorisation of 2068 Prime factorisation of 2708 Prime factorisation of 1144 Prime factorisation of 2460 Prime factorisation of 2052
✅ Answer key — Prime factorisation
2 × 5² × 23 2² × 61 2² × 347 2 × 3 × 19² 2² × 7 × 29 2² × 11 × 47 2² × 677 2³ × 11 × 13 2² × 3 × 5 × 41 2² × 3³ × 19 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF and LCM Class 10 · Worksheet 2 · set 54
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 24 and 32 HCF and LCM of 99 and 108 HCF and LCM of 28 and 210 HCF and LCM of 100 and 140 HCF and LCM of 99 and 110 HCF and LCM of 18 and 45 HCF and LCM of 4 and 22 HCF and LCM of 30 and 70
✅ Answer key — HCF and LCM
HCF = 8, LCM = 96 HCF = 9, LCM = 1188 HCF = 14, LCM = 420 HCF = 20, LCM = 700 HCF = 11, LCM = 990 HCF = 9, LCM = 90 HCF = 2, LCM = 44 HCF = 10, LCM = 210 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Euclid’s division algorithm Class 10 · Worksheet 3 · set 54
Name: Date: Score: / 8
Find the HCF.
HCF of 492 and 384 (Euclid’s division algorithm) HCF of 663 and 170 (Euclid’s division algorithm) HCF of 636 and 360 (Euclid’s division algorithm) HCF of 192 and 152 (Euclid’s division algorithm) HCF of 525 and 500 (Euclid’s division algorithm) HCF of 144 and 100 (Euclid’s division algorithm) HCF of 495 and 468 (Euclid’s division algorithm) HCF of 608 and 320 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
12 17 12 8 25 4 9 32 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF × LCM = product Class 10 · Worksheet 4 · set 54
Name: Date: Score: / 6
Solve.
HCF of two numbers is 8 and their LCM is 320. One number is 40. Find the other. HCF of two numbers is 13 and their LCM is 286. One number is 26. Find the other. HCF of two numbers is 9 and their LCM is 252. One number is 36. Find the other. HCF of two numbers is 8 and their LCM is 704. One number is 88. Find the other. HCF of two numbers is 7 and their LCM is 154. One number is 14. Find the other. HCF of two numbers is 5 and their LCM is 420. One number is 35. Find the other.
✅ Answer key — HCF × LCM = product
64 143 63 64 77 60 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Terminating decimals Class 10 · Worksheet 5 · set 54
Name: Date: Score: / 8
Answer without long division.
Does 73/25 have a terminating decimal expansion? Does 89/1625 have a terminating decimal expansion? Does 1023/400 have a terminating decimal expansion? Does 5/4 have a terminating decimal expansion? Does 477/560 have a terminating decimal expansion? Does 593/260 have a terminating decimal expansion? Does 109/208 have a terminating decimal expansion? Does 21/16 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 2²) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2⁴) TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Rational or irrational? Class 9–10 · Worksheet 6 · set 54
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 8√77 Rational or irrational: 4√100 Rational or irrational: 4√54 Rational or irrational: √96 Rational or irrational: 2√36 Rational or irrational: 7√78 Rational or irrational: √45 Rational or irrational: 4 + √5 Rational or irrational: 2√65 Rational or irrational: 1 + √3 Rational or irrational: 1 + √17 Rational or irrational: 7√49
✅ Answer key — Rational or irrational?
irrational rational irrational irrational rational irrational irrational irrational irrational irrational irrational rational TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Questions
What is the relation between HCF and LCM? For two positive integers a and b: HCF(a, b) × LCM(a, b) = a × b.
Are these worksheets free? Yes — print them or save as PDF free. Every worksheet has an answer key.
How do I get different questions? Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).
How do I print only one worksheet? Press “🖨️ Print” on that worksheet. Tick “with answer key” if you want the answers on a second page.
Can my child do this worksheet online, like a quiz? Yes — press “▶️ Practise online” on any worksheet. The questions come one at a time with instant marking, a score at the end and a review of mistakes. No sign-in is needed.
