Free · Class 10 · 6 worksheets · answer keys · practise online · set 43
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 43
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2784 Prime factorisation of 1533 Prime factorisation of 2472 Prime factorisation of 2726 Prime factorisation of 256 Prime factorisation of 2806 Prime factorisation of 285 Prime factorisation of 1824 Prime factorisation of 2070 Prime factorisation of 1624
✅ Answer key — Prime factorisation
2⁵ × 3 × 29 3 × 7 × 73 2³ × 3 × 103 2 × 29 × 47 2⁸ 2 × 23 × 61 3 × 5 × 19 2⁵ × 3 × 19 2 × 3² × 5 × 23 2³ × 7 × 29 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 43
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 76 and 171 HCF and LCM of 65 and 75 HCF and LCM of 10 and 24 HCF and LCM of 80 and 260 HCF and LCM of 56 and 63 HCF and LCM of 121 and 132 HCF and LCM of 14 and 35 HCF and LCM of 96 and 104
✅ Answer key — HCF and LCM
HCF = 19, LCM = 684 HCF = 5, LCM = 975 HCF = 2, LCM = 120 HCF = 20, LCM = 1040 HCF = 7, LCM = 504 HCF = 11, LCM = 1452 HCF = 7, LCM = 70 HCF = 8, LCM = 1248 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 43
Name: Date: Score: / 8
Find the HCF.
HCF of 539 and 132 (Euclid’s division algorithm) HCF of 378 and 243 (Euclid’s division algorithm) HCF of 855 and 480 (Euclid’s division algorithm) HCF of 476 and 392 (Euclid’s division algorithm) HCF of 988 and 342 (Euclid’s division algorithm) HCF of 961 and 279 (Euclid’s division algorithm) HCF of 825 and 528 (Euclid’s division algorithm) HCF of 528 and 456 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
11 27 15 28 38 31 33 24 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 43
Name: Date: Score: / 6
Solve.
HCF of two numbers is 10 and their LCM is 360. One number is 90. Find the other. HCF of two numbers is 6 and their LCM is 168. One number is 24. Find the other. HCF of two numbers is 12 and their LCM is 1008. One number is 144. Find the other. HCF of two numbers is 13 and their LCM is 455. One number is 91. Find the other. HCF of two numbers is 6 and their LCM is 330. One number is 30. Find the other. HCF of two numbers is 14 and their LCM is 308. One number is 28. Find the other.
✅ Answer key — HCF × LCM = product
40 42 84 65 66 154 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 43
Name: Date: Score: / 8
Answer without long division.
Does 33/40 have a terminating decimal expansion? Does 15/26 have a terminating decimal expansion? Does 39/40 have a terminating decimal expansion? Does 1291/1400 have a terminating decimal expansion? Does 547/400 have a terminating decimal expansion? Does 111/40 have a terminating decimal expansion? Does 111/50 have a terminating decimal expansion? Does 7/5 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 2³ × 5) Yes — terminating (denominator 2 × 5²) Yes — terminating (denominator 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 43
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √48 Rational or irrational: 9√4 Rational or irrational: √51 Rational or irrational: √10 Rational or irrational: √66 Rational or irrational: 3 + √49 Rational or irrational: 9 + √5 Rational or irrational: 2√97 Rational or irrational: 6√20 Rational or irrational: 4 + √89 Rational or irrational: 2 + √95 Rational or irrational: 4√87
✅ Answer key — Rational or irrational?
irrational rational irrational 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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