Free · Class 10 · 6 worksheets · answer keys · practise online · set 27
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 27
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2512 Prime factorisation of 1288 Prime factorisation of 2187 Prime factorisation of 506 Prime factorisation of 1098 Prime factorisation of 2805 Prime factorisation of 2739 Prime factorisation of 1940 Prime factorisation of 1548 Prime factorisation of 2450
✅ Answer key — Prime factorisation
2⁴ × 157 2³ × 7 × 23 3⁷ 2 × 11 × 23 2 × 3² × 61 3 × 5 × 11 × 17 3 × 11 × 83 2² × 5 × 97 2² × 3² × 43 2 × 5² × 7² TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 27
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 52 and 143 HCF and LCM of 36 and 117 HCF and LCM of 72 and 81 HCF and LCM of 12 and 28 HCF and LCM of 36 and 48 HCF and LCM of 64 and 112 HCF and LCM of 20 and 26 HCF and LCM of 154 and 182
✅ Answer key — HCF and LCM
HCF = 13, LCM = 572 HCF = 9, LCM = 468 HCF = 9, LCM = 648 HCF = 4, LCM = 84 HCF = 12, LCM = 144 HCF = 16, LCM = 448 HCF = 2, LCM = 260 HCF = 14, LCM = 2002 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 27
Name: Date: Score: / 8
Find the HCF.
HCF of 533 and 338 (Euclid’s division algorithm) HCF of 912 and 208 (Euclid’s division algorithm) HCF of 800 and 416 (Euclid’s division algorithm) HCF of 741 and 722 (Euclid’s division algorithm) HCF of 900 and 342 (Euclid’s division algorithm) HCF of 520 and 100 (Euclid’s division algorithm) HCF of 987 and 252 (Euclid’s division algorithm) HCF of 329 and 147 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
13 16 32 19 18 20 21 7 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 27
Name: Date: Score: / 6
Solve.
HCF of two numbers is 2 and their LCM is 20. One number is 4. Find the other. HCF of two numbers is 5 and their LCM is 495. One number is 55. Find the other. HCF of two numbers is 13 and their LCM is 1287. One number is 117. Find the other. HCF of two numbers is 10 and their LCM is 880. One number is 80. Find the other. HCF of two numbers is 9 and their LCM is 198. One number is 18. Find the other. HCF of two numbers is 4 and their LCM is 84. One number is 12. Find the other.
✅ Answer key — HCF × LCM = product
10 45 143 110 99 28 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 27
Name: Date: Score: / 8
Answer without long division.
Does 79/30 have a terminating decimal expansion? Does 5/4 have a terminating decimal expansion? Does 54/25 have a terminating decimal expansion? Does 5/14 have a terminating decimal expansion? Does 59/55 have a terminating decimal expansion? Does 83/300 have a terminating decimal expansion? Does 91/120 have a terminating decimal expansion? Does 724/625 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2²) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5⁴) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 27
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √73 Rational or irrational: √58 Rational or irrational: 2√88 Rational or irrational: √97 Rational or irrational: 5√12 Rational or irrational: √55 Rational or irrational: 2√29 Rational or irrational: 4 + √64 Rational or irrational: 6√31 Rational or irrational: 4√26 Rational or irrational: 1√98 Rational or irrational: 6 + √32
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational rational 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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