Free · Class 10 · 6 worksheets · answer keys · practise online · set 50
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 50
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1194 Prime factorisation of 1813 Prime factorisation of 1010 Prime factorisation of 2882 Prime factorisation of 2702 Prime factorisation of 2368 Prime factorisation of 768 Prime factorisation of 1737 Prime factorisation of 988 Prime factorisation of 1935
✅ Answer key — Prime factorisation
2 × 3 × 199 7² × 37 2 × 5 × 101 2 × 11 × 131 2 × 7 × 193 2⁶ × 37 2⁸ × 3 3² × 193 2² × 13 × 19 3² × 5 × 43 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF and LCM Class 10 · Worksheet 2 · set 50
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 30 and 36 HCF and LCM of 60 and 135 HCF and LCM of 35 and 49 HCF and LCM of 64 and 104 HCF and LCM of 32 and 72 HCF and LCM of 48 and 78 HCF and LCM of 28 and 60 HCF and LCM of 42 and 90
✅ Answer key — HCF and LCM
HCF = 6, LCM = 180 HCF = 15, LCM = 540 HCF = 7, LCM = 245 HCF = 8, LCM = 832 HCF = 8, LCM = 288 HCF = 6, LCM = 624 HCF = 4, LCM = 420 HCF = 6, LCM = 630 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 50
Name: Date: Score: / 8
Find the HCF.
HCF of 286 and 110 (Euclid’s division algorithm) HCF of 816 and 312 (Euclid’s division algorithm) HCF of 288 and 225 (Euclid’s division algorithm) HCF of 150 and 144 (Euclid’s division algorithm) HCF of 799 and 374 (Euclid’s division algorithm) HCF of 273 and 130 (Euclid’s division algorithm) HCF of 714 and 493 (Euclid’s division algorithm) HCF of 410 and 390 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
22 24 9 6 17 13 17 10 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF × LCM = product Class 10 · Worksheet 4 · set 50
Name: Date: Score: / 6
Solve.
HCF of two numbers is 2 and their LCM is 120. One number is 10. Find the other. HCF of two numbers is 11 and their LCM is 264. One number is 88. Find the other. HCF of two numbers is 4 and their LCM is 96. One number is 32. Find the other. HCF of two numbers is 12 and their LCM is 756. One number is 84. Find the other. HCF of two numbers is 3 and their LCM is 297. One number is 27. Find the other. HCF of two numbers is 5 and their LCM is 315. One number is 35. Find the other.
✅ Answer key — HCF × LCM = product
24 33 12 108 33 45 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Terminating decimals Class 10 · Worksheet 5 · set 50
Name: Date: Score: / 8
Answer without long division.
Does 413/250 have a terminating decimal expansion? Does 253/250 have a terminating decimal expansion? Does 494/875 have a terminating decimal expansion? Does 1/52 have a terminating decimal expansion? Does 371/400 have a terminating decimal expansion? Does 87/50 have a terminating decimal expansion? Does 247/400 have a terminating decimal expansion? Does 9/16 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2 × 5³) Yes — terminating (denominator 2 × 5³) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 2 × 5²) Yes — terminating (denominator 2⁴ × 5²) 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 50
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 5√59 Rational or irrational: √51 Rational or irrational: 8√37 Rational or irrational: 1√5 Rational or irrational: 3√23 Rational or irrational: √71 Rational or irrational: √44 Rational or irrational: √64 Rational or irrational: 7 + √15 Rational or irrational: 2 + √25 Rational or irrational: 8 + √19 Rational or irrational: 3 + √37
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational rational irrational rational 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.
