Free · Class 10 · 6 worksheets · answer keys · practise online · set 78
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 78
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2916 Prime factorisation of 968 Prime factorisation of 1732 Prime factorisation of 496 Prime factorisation of 1292 Prime factorisation of 165 Prime factorisation of 2575 Prime factorisation of 1252 Prime factorisation of 730 Prime factorisation of 300
✅ Answer key — Prime factorisation
2² × 3⁶ 2³ × 11² 2² × 433 2⁴ × 31 2² × 17 × 19 3 × 5 × 11 5² × 103 2² × 313 2 × 5 × 73 2² × 3 × 5² TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 78
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 24 and 39 HCF and LCM of 49 and 91 HCF and LCM of 88 and 143 HCF and LCM of 198 and 216 HCF and LCM of 20 and 70 HCF and LCM of 104 and 143 HCF and LCM of 24 and 90 HCF and LCM of 112 and 192
✅ Answer key — HCF and LCM
HCF = 3, LCM = 312 HCF = 7, LCM = 637 HCF = 11, LCM = 1144 HCF = 18, LCM = 2376 HCF = 10, LCM = 140 HCF = 13, LCM = 1144 HCF = 6, LCM = 360 HCF = 16, LCM = 1344 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 78
Name: Date: Score: / 8
Find the HCF.
HCF of 605 and 528 (Euclid’s division algorithm) HCF of 602 and 238 (Euclid’s division algorithm) HCF of 234 and 207 (Euclid’s division algorithm) HCF of 649 and 583 (Euclid’s division algorithm) HCF of 275 and 190 (Euclid’s division algorithm) HCF of 666 and 558 (Euclid’s division algorithm) HCF of 290 and 225 (Euclid’s division algorithm) HCF of 814 and 792 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
11 14 9 11 5 18 5 22 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 78
Name: Date: Score: / 6
Solve.
HCF of two numbers is 8 and their LCM is 48. One number is 24. Find the other. HCF of two numbers is 14 and their LCM is 420. One number is 70. Find the other. HCF of two numbers is 7 and their LCM is 588. One number is 84. Find the other. HCF of two numbers is 3 and their LCM is 216. One number is 24. Find the other. HCF of two numbers is 8 and their LCM is 672. One number is 96. Find the other. HCF of two numbers is 13 and their LCM is 468. One number is 52. Find the other.
✅ Answer key — HCF × LCM = product
16 84 49 27 56 117 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 78
Name: Date: Score: / 8
Answer without long division.
Does 1293/500 have a terminating decimal expansion? Does 7/12 have a terminating decimal expansion? Does 23/280 have a terminating decimal expansion? Does 971/700 have a terminating decimal expansion? Does 13/100 have a terminating decimal expansion? Does 367/140 have a terminating decimal expansion? Does 411/176 have a terminating decimal expansion? Does 33/80 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2² × 5³) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2² × 5²) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2⁴ × 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 78
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 6√60 Rational or irrational: √23 Rational or irrational: 9 + √73 Rational or irrational: 2√92 Rational or irrational: 9 + √88 Rational or irrational: 7 + √6 Rational or irrational: 4 + √72 Rational or irrational: √44 Rational or irrational: 9√80 Rational or irrational: 3 + √69 Rational or irrational: 9√76 Rational or irrational: 2√87
✅ 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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