Free · Class 10 · 6 worksheets · answer keys · practise online · set 36
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 36
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 774 Prime factorisation of 642 Prime factorisation of 1705 Prime factorisation of 1503 Prime factorisation of 1647 Prime factorisation of 798 Prime factorisation of 1924 Prime factorisation of 2379 Prime factorisation of 1521 Prime factorisation of 872
✅ Answer key — Prime factorisation
2 × 3² × 43 2 × 3 × 107 5 × 11 × 31 3² × 167 3³ × 61 2 × 3 × 7 × 19 2² × 13 × 37 3 × 13 × 61 3² × 13² 2³ × 109 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 36
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 119 and 153 HCF and LCM of 12 and 90 HCF and LCM of 40 and 60 HCF and LCM of 27 and 42 HCF and LCM of 12 and 54 HCF and LCM of 70 and 154 HCF and LCM of 140 and 154 HCF and LCM of 36 and 168
✅ Answer key — HCF and LCM
HCF = 17, LCM = 1071 HCF = 6, LCM = 180 HCF = 20, LCM = 120 HCF = 3, LCM = 378 HCF = 6, LCM = 108 HCF = 14, LCM = 770 HCF = 14, LCM = 1540 HCF = 12, LCM = 504 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 36
Name: Date: Score: / 8
Find the HCF.
HCF of 550 and 154 (Euclid’s division algorithm) HCF of 215 and 155 (Euclid’s division algorithm) HCF of 630 and 288 (Euclid’s division algorithm) HCF of 625 and 300 (Euclid’s division algorithm) HCF of 640 and 120 (Euclid’s division algorithm) HCF of 893 and 399 (Euclid’s division algorithm) HCF of 322 and 126 (Euclid’s division algorithm) HCF of 364 and 322 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
22 5 18 25 40 19 14 14 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 36
Name: Date: Score: / 6
Solve.
HCF of two numbers is 13 and their LCM is 468. One number is 52. Find the other. HCF of two numbers is 2 and their LCM is 168. One number is 14. Find the other. HCF of two numbers is 2 and their LCM is 90. One number is 10. Find the other. HCF of two numbers is 3 and their LCM is 63. One number is 21. Find the other. HCF of two numbers is 4 and their LCM is 288. One number is 32. Find the other. HCF of two numbers is 9 and their LCM is 810. One number is 81. Find the other.
✅ Answer key — HCF × LCM = product
117 24 18 9 36 90 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 36
Name: Date: Score: / 8
Answer without long division.
Does 104/125 have a terminating decimal expansion? Does 147/50 have a terminating decimal expansion? Does 508/325 have a terminating decimal expansion? Does 23/65 have a terminating decimal expansion? Does 525/208 have a terminating decimal expansion? Does 713/375 have a terminating decimal expansion? Does 62/25 have a terminating decimal expansion? Does 29/30 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5³) Yes — terminating (denominator 2 × 5²) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 3) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 36
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 3 + √55 Rational or irrational: √42 Rational or irrational: 5√5 Rational or irrational: √29 Rational or irrational: 6√36 Rational or irrational: 2 + √14 Rational or irrational: √56 Rational or irrational: 3√63 Rational or irrational: 4 + √89 Rational or irrational: 9√96 Rational or irrational: √92 Rational or irrational: 4 + √11
✅ 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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