Free · Class 10 · 6 worksheets · answer keys · practise online · set 47
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 47
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1443 Prime factorisation of 2432 Prime factorisation of 288 Prime factorisation of 2776 Prime factorisation of 1500 Prime factorisation of 1656 Prime factorisation of 867 Prime factorisation of 343 Prime factorisation of 2050 Prime factorisation of 2331
✅ Answer key — Prime factorisation
3 × 13 × 37 2⁷ × 19 2⁵ × 3² 2³ × 347 2² × 3 × 5³ 2³ × 3² × 23 3 × 17² 7³ 2 × 5² × 41 3² × 7 × 37 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF and LCM Class 10 · Worksheet 2 · set 47
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 40 and 180 HCF and LCM of 54 and 78 HCF and LCM of 20 and 90 HCF and LCM of 27 and 72 HCF and LCM of 42 and 78 HCF and LCM of 70 and 77 HCF and LCM of 100 and 140 HCF and LCM of 133 and 171
✅ Answer key — HCF and LCM
HCF = 20, LCM = 360 HCF = 6, LCM = 702 HCF = 10, LCM = 180 HCF = 9, LCM = 216 HCF = 6, LCM = 546 HCF = 7, LCM = 770 HCF = 20, LCM = 700 HCF = 19, LCM = 1197 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 47
Name: Date: Score: / 8
Find the HCF.
HCF of 812 and 112 (Euclid’s division algorithm) HCF of 484 and 297 (Euclid’s division algorithm) HCF of 216 and 100 (Euclid’s division algorithm) HCF of 696 and 624 (Euclid’s division algorithm) HCF of 636 and 192 (Euclid’s division algorithm) HCF of 832 and 338 (Euclid’s division algorithm) HCF of 672 and 256 (Euclid’s division algorithm) HCF of 928 and 480 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
28 11 4 24 12 26 32 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 47
Name: Date: Score: / 6
Solve.
HCF of two numbers is 6 and their LCM is 120. One number is 24. Find the other. HCF of two numbers is 6 and their LCM is 420. One number is 60. Find the other. HCF of two numbers is 11 and their LCM is 462. One number is 77. Find the other. HCF of two numbers is 5 and their LCM is 440. One number is 55. Find the other. HCF of two numbers is 4 and their LCM is 120. One number is 12. Find the other. HCF of two numbers is 14 and their LCM is 1078. One number is 98. Find the other.
✅ Answer key — HCF × LCM = product
30 42 66 40 40 154 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Terminating decimals Class 10 · Worksheet 5 · set 47
Name: Date: Score: / 8
Answer without long division.
Does 191/100 have a terminating decimal expansion? Does 237/400 have a terminating decimal expansion? Does 35/16 have a terminating decimal expansion? Does 1177/500 have a terminating decimal expansion? Does 3/4 have a terminating decimal expansion? Does 5/2 have a terminating decimal expansion? Does 2153/1000 have a terminating decimal expansion? Does 36/25 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2² × 5²) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 2² × 5³) Yes — terminating (denominator 2²) Yes — terminating (denominator 2) Yes — terminating (denominator 2³ × 5³) Yes — terminating (denominator 5²) 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 47
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √29 Rational or irrational: √85 Rational or irrational: √75 Rational or irrational: 4 + √50 Rational or irrational: 5√54 Rational or irrational: 4√71 Rational or irrational: √2 Rational or irrational: 5 + √8 Rational or irrational: √68 Rational or irrational: 4 + √41 Rational or irrational: 6√38 Rational or irrational: 5√85
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational irrational irrational irrational irrational irrational 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.
