Free · Class 10 · 6 worksheets · answer keys · practise online · set 14
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 14
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 672 Prime factorisation of 2236 Prime factorisation of 2667 Prime factorisation of 2770 Prime factorisation of 2884 Prime factorisation of 1190 Prime factorisation of 246 Prime factorisation of 652 Prime factorisation of 1704 Prime factorisation of 2080
✅ Answer key — Prime factorisation
2⁵ × 3 × 7 2² × 13 × 43 3 × 7 × 127 2 × 5 × 277 2² × 7 × 103 2 × 5 × 7 × 17 2 × 3 × 41 2² × 163 2³ × 3 × 71 2⁵ × 5 × 13 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 14
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 160 and 208 HCF and LCM of 27 and 33 HCF and LCM of 42 and 112 HCF and LCM of 112 and 126 HCF and LCM of 24 and 44 HCF and LCM of 64 and 176 HCF and LCM of 32 and 72 HCF and LCM of 51 and 238
✅ Answer key — HCF and LCM
HCF = 16, LCM = 2080 HCF = 3, LCM = 297 HCF = 14, LCM = 336 HCF = 14, LCM = 1008 HCF = 4, LCM = 264 HCF = 16, LCM = 704 HCF = 8, LCM = 288 HCF = 17, LCM = 714 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 14
Name: Date: Score: / 8
Find the HCF.
HCF of 120 and 116 (Euclid’s division algorithm) HCF of 231 and 133 (Euclid’s division algorithm) HCF of 490 and 322 (Euclid’s division algorithm) HCF of 920 and 720 (Euclid’s division algorithm) HCF of 405 and 345 (Euclid’s division algorithm) HCF of 378 and 203 (Euclid’s division algorithm) HCF of 770 and 175 (Euclid’s division algorithm) HCF of 279 and 126 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
4 7 14 40 15 7 35 9 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 14
Name: Date: Score: / 6
Solve.
HCF of two numbers is 13 and their LCM is 1430. One number is 130. Find the other. HCF of two numbers is 12 and their LCM is 1584. One number is 144. Find the other. HCF of two numbers is 11 and their LCM is 660. One number is 132. Find the other. HCF of two numbers is 3 and their LCM is 189. One number is 27. Find the other. HCF of two numbers is 6 and their LCM is 90. One number is 30. Find the other. HCF of two numbers is 3 and their LCM is 90. One number is 15. Find the other.
✅ Answer key — HCF × LCM = product
143 132 55 21 18 18 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 14
Name: Date: Score: / 8
Answer without long division.
Does 5/2 have a terminating decimal expansion? Does 17/14 have a terminating decimal expansion? Does 137/88 have a terminating decimal expansion? Does 357/200 have a terminating decimal expansion? Does 599/350 have a terminating decimal expansion? Does 29/10 have a terminating decimal expansion? Does 129/55 have a terminating decimal expansion? Does 27/25 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2³ × 5²) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2 × 5) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 14
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √61 Rational or irrational: √80 Rational or irrational: 3 + √78 Rational or irrational: 3√6 Rational or irrational: 9 + √34 Rational or irrational: 3√44 Rational or irrational: 3 + √83 Rational or irrational: 7 + √75 Rational or irrational: 2√37 Rational or irrational: √8 Rational or irrational: 7 + √73 Rational or irrational: 7√99
✅ 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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