Free · Class 10 · 6 worksheets · answer keys · practise online · set 88
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 88
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 658 Prime factorisation of 1715 Prime factorisation of 616 Prime factorisation of 1490 Prime factorisation of 410 Prime factorisation of 812 Prime factorisation of 1998 Prime factorisation of 1728 Prime factorisation of 1004 Prime factorisation of 324
✅ Answer key — Prime factorisation
2 × 7 × 47 5 × 7³ 2³ × 7 × 11 2 × 5 × 149 2 × 5 × 41 2² × 7 × 29 2 × 3³ × 37 2⁶ × 3³ 2² × 251 2² × 3⁴ TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 88
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 65 and 91 HCF and LCM of 8 and 28 HCF and LCM of 80 and 112 HCF and LCM of 84 and 120 HCF and LCM of 190 and 209 HCF and LCM of 32 and 60 HCF and LCM of 210 and 225 HCF and LCM of 12 and 78
✅ Answer key — HCF and LCM
HCF = 13, LCM = 455 HCF = 4, LCM = 56 HCF = 16, LCM = 560 HCF = 12, LCM = 840 HCF = 19, LCM = 2090 HCF = 4, LCM = 480 HCF = 15, LCM = 3150 HCF = 6, LCM = 156 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 88
Name: Date: Score: / 8
Find the HCF.
HCF of 387 and 261 (Euclid’s division algorithm) HCF of 840 and 270 (Euclid’s division algorithm) HCF of 360 and 296 (Euclid’s division algorithm) HCF of 252 and 224 (Euclid’s division algorithm) HCF of 754 and 319 (Euclid’s division algorithm) HCF of 960 and 620 (Euclid’s division algorithm) HCF of 493 and 348 (Euclid’s division algorithm) HCF of 295 and 100 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
9 30 8 28 29 20 29 5 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 88
Name: Date: Score: / 6
Solve.
HCF of two numbers is 15 and their LCM is 315. One number is 45. Find the other. HCF of two numbers is 9 and their LCM is 792. One number is 99. Find the other. HCF of two numbers is 12 and their LCM is 264. One number is 24. Find the other. HCF of two numbers is 4 and their LCM is 120. One number is 24. Find the other. HCF of two numbers is 14 and their LCM is 462. One number is 42. Find the other. HCF of two numbers is 13 and their LCM is 390. One number is 130. Find the other.
✅ Answer key — HCF × LCM = product
105 72 132 20 154 39 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 88
Name: Date: Score: / 8
Answer without long division.
Does 36/25 have a terminating decimal expansion? Does 447/400 have a terminating decimal expansion? Does 953/600 have a terminating decimal expansion? Does 271/500 have a terminating decimal expansion? Does 27/40 have a terminating decimal expansion? Does 14/25 have a terminating decimal expansion? Does 261/440 have a terminating decimal expansion? Does 9/10 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5²) Yes — terminating (denominator 2⁴ × 5²) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2² × 5³) Yes — terminating (denominator 2³ × 5) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2 × 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 88
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 1 + √38 Rational or irrational: 5√90 Rational or irrational: 5 + √26 Rational or irrational: √40 Rational or irrational: √9 Rational or irrational: 5√6 Rational or irrational: 1 + √44 Rational or irrational: 7 + √10 Rational or irrational: 6√54 Rational or irrational: 6 + √19 Rational or irrational: 6√91 Rational or irrational: √32
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational rational irrational 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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