Free · Class 10 · 6 worksheets · answer keys · practise online · set 38
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 38
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2375 Prime factorisation of 580 Prime factorisation of 1025 Prime factorisation of 596 Prime factorisation of 1998 Prime factorisation of 928 Prime factorisation of 2712 Prime factorisation of 2838 Prime factorisation of 1183 Prime factorisation of 1636
✅ Answer key — Prime factorisation
5³ × 19 2² × 5 × 29 5² × 41 2² × 149 2 × 3³ × 37 2⁵ × 29 2³ × 3 × 113 2 × 3 × 11 × 43 7 × 13² 2² × 409 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF and LCM Class 10 · Worksheet 2 · set 38
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 88 and 165 HCF and LCM of 15 and 25 HCF and LCM of 75 and 195 HCF and LCM of 126 and 234 HCF and LCM of 99 and 143 HCF and LCM of 112 and 208 HCF and LCM of 126 and 135 HCF and LCM of 36 and 90
✅ Answer key — HCF and LCM
HCF = 11, LCM = 1320 HCF = 5, LCM = 75 HCF = 15, LCM = 975 HCF = 18, LCM = 1638 HCF = 11, LCM = 1287 HCF = 16, LCM = 1456 HCF = 9, LCM = 1890 HCF = 18, LCM = 180 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 38
Name: Date: Score: / 8
Find the HCF.
HCF of 424 and 224 (Euclid’s division algorithm) HCF of 280 and 170 (Euclid’s division algorithm) HCF of 984 and 312 (Euclid’s division algorithm) HCF of 512 and 176 (Euclid’s division algorithm) HCF of 645 and 525 (Euclid’s division algorithm) HCF of 532 and 285 (Euclid’s division algorithm) HCF of 392 and 182 (Euclid’s division algorithm) HCF of 735 and 455 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
8 10 24 16 15 19 14 35 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF × LCM = product Class 10 · Worksheet 4 · set 38
Name: Date: Score: / 6
Solve.
HCF of two numbers is 3 and their LCM is 198. One number is 18. Find the other. HCF of two numbers is 4 and their LCM is 160. One number is 20. Find the other. HCF of two numbers is 9 and their LCM is 270. One number is 90. Find the other. HCF of two numbers is 12 and their LCM is 252. One number is 84. Find the other. HCF of two numbers is 7 and their LCM is 315. One number is 35. Find the other. HCF of two numbers is 14 and their LCM is 392. One number is 98. Find the other.
✅ Answer key — HCF × LCM = product
33 32 27 36 63 56 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Terminating decimals Class 10 · Worksheet 5 · set 38
Name: Date: Score: / 8
Answer without long division.
Does 901/550 have a terminating decimal expansion? Does 257/112 have a terminating decimal expansion? Does 591/500 have a terminating decimal expansion? Does 199/125 have a terminating decimal expansion? Does 5/2 have a terminating decimal expansion? Does 1827/625 have a terminating decimal expansion? Does 71/25 have a terminating decimal expansion? Does 1/2 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2² × 5³) Yes — terminating (denominator 5³) Yes — terminating (denominator 2) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 5²) Yes — terminating (denominator 2) 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 38
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 2 + √78 Rational or irrational: 4 + √45 Rational or irrational: √61 Rational or irrational: √2 Rational or irrational: 2 + √48 Rational or irrational: √30 Rational or irrational: 8 + √16 Rational or irrational: 2√32 Rational or irrational: 8√81 Rational or irrational: 2 + √20 Rational or irrational: 7√29 Rational or irrational: √60
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational rational irrational rational 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.
