Free · Class 10 · 6 worksheets · answer keys · practise online · set 12
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 12
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1738 Prime factorisation of 2889 Prime factorisation of 2456 Prime factorisation of 2912 Prime factorisation of 2810 Prime factorisation of 1648 Prime factorisation of 656 Prime factorisation of 1796 Prime factorisation of 1215 Prime factorisation of 2886
✅ Answer key — Prime factorisation
2 × 11 × 79 3³ × 107 2³ × 307 2⁵ × 7 × 13 2 × 5 × 281 2⁴ × 103 2⁴ × 41 2² × 449 3⁵ × 5 2 × 3 × 13 × 37 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 12
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 24 and 32 HCF and LCM of 75 and 210 HCF and LCM of 39 and 52 HCF and LCM of 57 and 152 HCF and LCM of 140 and 300 HCF and LCM of 78 and 143 HCF and LCM of 9 and 30 HCF and LCM of 70 and 130
✅ Answer key — HCF and LCM
HCF = 8, LCM = 96 HCF = 15, LCM = 1050 HCF = 13, LCM = 156 HCF = 19, LCM = 456 HCF = 20, LCM = 2100 HCF = 13, LCM = 858 HCF = 3, LCM = 90 HCF = 10, LCM = 910 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 12
Name: Date: Score: / 8
Find the HCF.
HCF of 816 and 608 (Euclid’s division algorithm) HCF of 147 and 123 (Euclid’s division algorithm) HCF of 600 and 275 (Euclid’s division algorithm) HCF of 726 and 682 (Euclid’s division algorithm) HCF of 315 and 231 (Euclid’s division algorithm) HCF of 884 and 459 (Euclid’s division algorithm) HCF of 784 and 630 (Euclid’s division algorithm) HCF of 874 and 209 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
16 3 25 22 21 17 14 19 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 12
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 594. One number is 99. Find the other. HCF of two numbers is 5 and their LCM is 220. One number is 20. Find the other. HCF of two numbers is 3 and their LCM is 210. One number is 30. Find the other. HCF of two numbers is 4 and their LCM is 336. One number is 28. Find the other. HCF of two numbers is 2 and their LCM is 180. One number is 20. Find the other. HCF of two numbers is 7 and their LCM is 84. One number is 21. Find the other.
✅ Answer key — HCF × LCM = product
54 55 21 48 18 28 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 12
Name: Date: Score: / 8
Answer without long division.
Does 61/140 have a terminating decimal expansion? Does 3/35 have a terminating decimal expansion? Does 211/200 have a terminating decimal expansion? Does 831/1250 have a terminating decimal expansion? Does 171/70 have a terminating decimal expansion? Does 317/208 have a terminating decimal expansion? Does 5/2 have a terminating decimal expansion? Does 277/500 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 2 × 5⁴) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2) Yes — terminating (denominator 2² × 5³) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 12
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √53 Rational or irrational: 8√54 Rational or irrational: √41 Rational or irrational: √96 Rational or irrational: 8 + √16 Rational or irrational: √46 Rational or irrational: 4 + √97 Rational or irrational: 1 + √45 Rational or irrational: 6√7 Rational or irrational: 8 + √51 Rational or irrational: 2 + √63 Rational or irrational: 5 + √37
✅ 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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