Free · Class 10 · 6 worksheets · answer keys · practise online · set 68
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 68
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2292 Prime factorisation of 1292 Prime factorisation of 2046 Prime factorisation of 1572 Prime factorisation of 984 Prime factorisation of 885 Prime factorisation of 621 Prime factorisation of 1960 Prime factorisation of 520 Prime factorisation of 1848
✅ Answer key — Prime factorisation
2² × 3 × 191 2² × 17 × 19 2 × 3 × 11 × 31 2² × 3 × 131 2³ × 3 × 41 3 × 5 × 59 3³ × 23 2³ × 5 × 7² 2³ × 5 × 13 2³ × 3 × 7 × 11 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF and LCM Class 10 · Worksheet 2 · set 68
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 55 and 66 HCF and LCM of 105 and 120 HCF and LCM of 165 and 225 HCF and LCM of 6 and 22 HCF and LCM of 228 and 247 HCF and LCM of 39 and 42 HCF and LCM of 15 and 24 HCF and LCM of 119 and 153
✅ Answer key — HCF and LCM
HCF = 11, LCM = 330 HCF = 15, LCM = 840 HCF = 15, LCM = 2475 HCF = 2, LCM = 66 HCF = 19, LCM = 2964 HCF = 3, LCM = 546 HCF = 3, LCM = 120 HCF = 17, LCM = 1071 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 68
Name: Date: Score: / 8
Find the HCF.
HCF of 675 and 480 (Euclid’s division algorithm) HCF of 864 and 272 (Euclid’s division algorithm) HCF of 527 and 170 (Euclid’s division algorithm) HCF of 522 and 203 (Euclid’s division algorithm) HCF of 328 and 272 (Euclid’s division algorithm) HCF of 627 and 266 (Euclid’s division algorithm) HCF of 688 and 352 (Euclid’s division algorithm) HCF of 342 and 192 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
15 16 17 29 8 19 16 6 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF × LCM = product Class 10 · Worksheet 4 · set 68
Name: Date: Score: / 6
Solve.
HCF of two numbers is 11 and their LCM is 1210. One number is 110. Find the other. HCF of two numbers is 14 and their LCM is 1540. One number is 154. Find the other. HCF of two numbers is 7 and their LCM is 588. One number is 49. Find the other. HCF of two numbers is 13 and their LCM is 910. One number is 91. Find the other. HCF of two numbers is 6 and their LCM is 168. One number is 24. Find the other. HCF of two numbers is 7 and their LCM is 294. One number is 42. Find the other.
✅ Answer key — HCF × LCM = product
121 140 84 130 42 49 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Terminating decimals Class 10 · Worksheet 5 · set 68
Name: Date: Score: / 8
Answer without long division.
Does 551/2000 have a terminating decimal expansion? Does 1999/1300 have a terminating decimal expansion? Does 225/112 have a terminating decimal expansion? Does 106/125 have a terminating decimal expansion? Does 61/220 have a terminating decimal expansion? Does 3/5 have a terminating decimal expansion? Does 2257/2000 have a terminating decimal expansion? Does 169/700 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2⁴ × 5³) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5) Yes — terminating (denominator 2⁴ × 5³) No — non-terminating repeating (denominator has the factor 7) 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 68
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 8 + √51 Rational or irrational: 7√100 Rational or irrational: √2 Rational or irrational: 4√42 Rational or irrational: √93 Rational or irrational: 2 + √18 Rational or irrational: 1 + √94 Rational or irrational: 3√16 Rational or irrational: 2 + √56 Rational or irrational: √78 Rational or irrational: √69 Rational or irrational: √94
✅ Answer key — Rational or irrational?
irrational rational irrational irrational irrational irrational irrational rational 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.
