Free · Class 10 · 6 worksheets · answer keys · practise online · set 10
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.
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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 10
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1331 Prime factorisation of 888 Prime factorisation of 438 Prime factorisation of 2036 Prime factorisation of 2564 Prime factorisation of 1455 Prime factorisation of 1644 Prime factorisation of 2922 Prime factorisation of 518 Prime factorisation of 1276
✅ Answer key — Prime factorisation
11³ 2³ × 3 × 37 2 × 3 × 73 2² × 509 2² × 641 3 × 5 × 97 2² × 3 × 137 2 × 3 × 487 2 × 7 × 37 2² × 11 × 29 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 10
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 120 and 225 HCF and LCM of 30 and 195 HCF and LCM of 85 and 136 HCF and LCM of 66 and 72 HCF and LCM of 26 and 195 HCF and LCM of 10 and 24 HCF and LCM of 91 and 195 HCF and LCM of 85 and 204
✅ Answer key — HCF and LCM
HCF = 15, LCM = 1800 HCF = 15, LCM = 390 HCF = 17, LCM = 680 HCF = 6, LCM = 792 HCF = 13, LCM = 390 HCF = 2, LCM = 120 HCF = 13, LCM = 1365 HCF = 17, LCM = 1020 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 10
Name: Date: Score: / 8
Find the HCF.
HCF of 874 and 589 (Euclid’s division algorithm) HCF of 560 and 120 (Euclid’s division algorithm) HCF of 240 and 108 (Euclid’s division algorithm) HCF of 689 and 559 (Euclid’s division algorithm) HCF of 396 and 180 (Euclid’s division algorithm) HCF of 312 and 128 (Euclid’s division algorithm) HCF of 663 and 170 (Euclid’s division algorithm) HCF of 952 and 323 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
19 40 12 13 36 8 17 17 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 10
Name: Date: Score: / 6
Solve.
HCF of two numbers is 3 and their LCM is 165. One number is 33. Find the other. HCF of two numbers is 8 and their LCM is 352. One number is 32. Find the other. HCF of two numbers is 9 and their LCM is 540. One number is 45. Find the other. HCF of two numbers is 3 and their LCM is 210. One number is 21. Find the other. HCF of two numbers is 10 and their LCM is 600. One number is 50. Find the other. HCF of two numbers is 13 and their LCM is 1716. One number is 156. Find the other.
✅ Answer key — HCF × LCM = product
15 88 108 30 120 143 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 10
Name: Date: Score: / 8
Answer without long division.
Does 37/25 have a terminating decimal expansion? Does 32/25 have a terminating decimal expansion? Does 543/350 have a terminating decimal expansion? Does 2157/880 have a terminating decimal expansion? Does 636/625 have a terminating decimal expansion? Does 23/24 have a terminating decimal expansion? Does 23/22 have a terminating decimal expansion? Does 211/125 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5²) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5³) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 10
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 1√87 Rational or irrational: √42 Rational or irrational: 5 + √16 Rational or irrational: √76 Rational or irrational: √34 Rational or irrational: √36 Rational or irrational: 4√86 Rational or irrational: √10 Rational or irrational: 9 + √51 Rational or irrational: 8 + √75 Rational or irrational: √23 Rational or irrational: 8 + √80
✅ Answer key — Rational or irrational?
irrational irrational rational irrational irrational rational irrational irrational irrational irrational irrational irrational TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Questions
What is the relation between HCF and LCM? For two positive integers a and b: HCF(a, b) × LCM(a, b) = a × b.
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