Free · Class 10 · 6 worksheets · answer keys · practise online · set 16
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 16
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1544 Prime factorisation of 120 Prime factorisation of 290 Prime factorisation of 1630 Prime factorisation of 924 Prime factorisation of 2112 Prime factorisation of 1729 Prime factorisation of 470 Prime factorisation of 528 Prime factorisation of 424
✅ Answer key — Prime factorisation
2³ × 193 2³ × 3 × 5 2 × 5 × 29 2 × 5 × 163 2² × 3 × 7 × 11 2⁶ × 3 × 11 7 × 13 × 19 2 × 5 × 47 2⁴ × 3 × 11 2³ × 53 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 16
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 21 and 49 HCF and LCM of 77 and 98 HCF and LCM of 80 and 128 HCF and LCM of 12 and 52 HCF and LCM of 34 and 221 HCF and LCM of 30 and 78 HCF and LCM of 15 and 36 HCF and LCM of 132 and 168
✅ Answer key — HCF and LCM
HCF = 7, LCM = 147 HCF = 7, LCM = 1078 HCF = 16, LCM = 640 HCF = 4, LCM = 156 HCF = 17, LCM = 442 HCF = 6, LCM = 390 HCF = 3, LCM = 180 HCF = 12, LCM = 1848 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 16
Name: Date: Score: / 8
Find the HCF.
HCF of 174 and 135 (Euclid’s division algorithm) HCF of 530 and 310 (Euclid’s division algorithm) HCF of 522 and 216 (Euclid’s division algorithm) HCF of 986 and 957 (Euclid’s division algorithm) HCF of 576 and 324 (Euclid’s division algorithm) HCF of 464 and 200 (Euclid’s division algorithm) HCF of 972 and 513 (Euclid’s division algorithm) HCF of 720 and 520 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
3 10 18 29 36 8 27 40 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 16
Name: Date: Score: / 6
Solve.
HCF of two numbers is 2 and their LCM is 42. One number is 6. Find the other. HCF of two numbers is 6 and their LCM is 210. One number is 30. Find the other. HCF of two numbers is 7 and their LCM is 385. One number is 35. Find the other. HCF of two numbers is 14 and their LCM is 504. One number is 126. Find the other. HCF of two numbers is 12 and their LCM is 504. One number is 72. Find the other. HCF of two numbers is 7 and their LCM is 490. One number is 49. Find the other.
✅ Answer key — HCF × LCM = product
14 42 77 56 84 70 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 16
Name: Date: Score: / 8
Answer without long division.
Does 137/125 have a terminating decimal expansion? Does 5/4 have a terminating decimal expansion? Does 1013/400 have a terminating decimal expansion? Does 11/20 have a terminating decimal expansion? Does 168/125 have a terminating decimal expansion? Does 139/48 have a terminating decimal expansion? Does 3399/1300 have a terminating decimal expansion? Does 7/16 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5³) Yes — terminating (denominator 2²) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 2² × 5) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2⁴) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 16
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √89 Rational or irrational: 9√27 Rational or irrational: √41 Rational or irrational: √90 Rational or irrational: 3 + √74 Rational or irrational: √45 Rational or irrational: 1 + √61 Rational or irrational: 4√33 Rational or irrational: 1√88 Rational or irrational: 6 + √79 Rational or irrational: 6 + √51 Rational or irrational: 5 + √71
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational 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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