Free · Class 10 · 6 worksheets · answer keys · practise online · set 59
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 59
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2541 Prime factorisation of 2872 Prime factorisation of 2849 Prime factorisation of 374 Prime factorisation of 994 Prime factorisation of 2152 Prime factorisation of 928 Prime factorisation of 2968 Prime factorisation of 1944 Prime factorisation of 560
✅ Answer key — Prime factorisation
3 × 7 × 11² 2³ × 359 7 × 11 × 37 2 × 11 × 17 2 × 7 × 71 2³ × 269 2⁵ × 29 2³ × 7 × 53 2³ × 3⁵ 2⁴ × 5 × 7 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF and LCM Class 10 · Worksheet 2 · set 59
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 72 and 126 HCF and LCM of 176 and 208 HCF and LCM of 209 and 247 HCF and LCM of 18 and 21 HCF and LCM of 180 and 234 HCF and LCM of 39 and 143 HCF and LCM of 48 and 54 HCF and LCM of 68 and 119
✅ Answer key — HCF and LCM
HCF = 18, LCM = 504 HCF = 16, LCM = 2288 HCF = 19, LCM = 2717 HCF = 3, LCM = 126 HCF = 18, LCM = 2340 HCF = 13, LCM = 429 HCF = 6, LCM = 432 HCF = 17, LCM = 476 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 59
Name: Date: Score: / 8
Find the HCF.
HCF of 637 and 416 (Euclid’s division algorithm) HCF of 814 and 154 (Euclid’s division algorithm) HCF of 468 and 264 (Euclid’s division algorithm) HCF of 690 and 437 (Euclid’s division algorithm) HCF of 507 and 390 (Euclid’s division algorithm) HCF of 423 and 333 (Euclid’s division algorithm) HCF of 784 and 496 (Euclid’s division algorithm) HCF of 899 and 145 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
13 22 12 23 39 9 16 29 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF × LCM = product Class 10 · Worksheet 4 · set 59
Name: Date: Score: / 6
Solve.
HCF of two numbers is 7 and their LCM is 539. One number is 49. Find the other. HCF of two numbers is 2 and their LCM is 126. One number is 14. Find the other. HCF of two numbers is 5 and their LCM is 90. One number is 45. Find the other. HCF of two numbers is 14 and their LCM is 140. One number is 70. Find the other. HCF of two numbers is 12 and their LCM is 240. One number is 48. Find the other. HCF of two numbers is 4 and their LCM is 140. One number is 28. Find the other.
✅ Answer key — HCF × LCM = product
77 18 10 28 60 20 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Terminating decimals Class 10 · Worksheet 5 · set 59
Name: Date: Score: / 8
Answer without long division.
Does 22/25 have a terminating decimal expansion? Does 179/100 have a terminating decimal expansion? Does 19/220 have a terminating decimal expansion? Does 1177/1300 have a terminating decimal expansion? Does 139/130 have a terminating decimal expansion? Does 66/25 have a terminating decimal expansion? Does 33/200 have a terminating decimal expansion? Does 1/100 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5²) Yes — terminating (denominator 2² × 5²) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5²) Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 2² × 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 59
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √65 Rational or irrational: 1 + √99 Rational or irrational: 9 + √77 Rational or irrational: √3 Rational or irrational: 6√38 Rational or irrational: 1 + √56 Rational or irrational: 6 + √65 Rational or irrational: 4√6 Rational or irrational: √68 Rational or irrational: 5√79 Rational or irrational: √88 Rational or irrational: √43
✅ 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.
