Free · Class 10 · 6 worksheets · answer keys · practise online · set 49
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 49
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 316 Prime factorisation of 2766 Prime factorisation of 2632 Prime factorisation of 2409 Prime factorisation of 418 Prime factorisation of 320 Prime factorisation of 348 Prime factorisation of 2756 Prime factorisation of 207 Prime factorisation of 2252
✅ Answer key — Prime factorisation
2² × 79 2 × 3 × 461 2³ × 7 × 47 3 × 11 × 73 2 × 11 × 19 2⁶ × 5 2² × 3 × 29 2² × 13 × 53 3² × 23 2² × 563 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF and LCM Class 10 · Worksheet 2 · set 49
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 35 and 45 HCF and LCM of 48 and 78 HCF and LCM of 4 and 6 HCF and LCM of 57 and 247 HCF and LCM of 133 and 247 HCF and LCM of 180 and 220 HCF and LCM of 40 and 88 HCF and LCM of 36 and 44
✅ Answer key — HCF and LCM
HCF = 5, LCM = 315 HCF = 6, LCM = 624 HCF = 2, LCM = 12 HCF = 19, LCM = 741 HCF = 19, LCM = 1729 HCF = 20, LCM = 1980 HCF = 8, LCM = 440 HCF = 4, LCM = 396 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 49
Name: Date: Score: / 8
Find the HCF.
HCF of 354 and 312 (Euclid’s division algorithm) HCF of 351 and 143 (Euclid’s division algorithm) HCF of 780 and 135 (Euclid’s division algorithm) HCF of 531 and 117 (Euclid’s division algorithm) HCF of 310 and 100 (Euclid’s division algorithm) HCF of 812 and 434 (Euclid’s division algorithm) HCF of 672 and 456 (Euclid’s division algorithm) HCF of 399 and 112 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
6 13 15 9 10 14 24 7 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF × LCM = product Class 10 · Worksheet 4 · set 49
Name: Date: Score: / 6
Solve.
HCF of two numbers is 10 and their LCM is 420. One number is 70. Find the other. HCF of two numbers is 2 and their LCM is 198. One number is 18. Find the other. HCF of two numbers is 4 and their LCM is 132. One number is 44. Find the other. HCF of two numbers is 4 and their LCM is 240. One number is 48. Find the other. HCF of two numbers is 14 and their LCM is 770. One number is 154. Find the other. HCF of two numbers is 13 and their LCM is 156. One number is 52. Find the other.
✅ Answer key — HCF × LCM = product
60 22 12 20 70 39 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Terminating decimals Class 10 · Worksheet 5 · set 49
Name: Date: Score: / 8
Answer without long division.
Does 1149/875 have a terminating decimal expansion? Does 306/125 have a terminating decimal expansion? Does 18/25 have a terminating decimal expansion? Does 94/125 have a terminating decimal expansion? Does 223/125 have a terminating decimal expansion? Does 217/125 have a terminating decimal expansion? Does 12/5 have a terminating decimal expansion? Does 13/6 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5³) Yes — terminating (denominator 5²) Yes — terminating (denominator 5³) Yes — terminating (denominator 5³) Yes — terminating (denominator 5³) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 3) 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 49
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 8√45 Rational or irrational: 2√43 Rational or irrational: 7 + √37 Rational or irrational: √80 Rational or irrational: √4 Rational or irrational: √53 Rational or irrational: √13 Rational or irrational: √14 Rational or irrational: 9 + √31 Rational or irrational: √44 Rational or irrational: 5 + √98 Rational or irrational: 9√95
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational rational 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.
