Free · Class 10 · 6 worksheets · answer keys · practise online · set 76
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 76
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2802 Prime factorisation of 2889 Prime factorisation of 1840 Prime factorisation of 1802 Prime factorisation of 1650 Prime factorisation of 2065 Prime factorisation of 1124 Prime factorisation of 2160 Prime factorisation of 2190 Prime factorisation of 1100
✅ Answer key — Prime factorisation
2 × 3 × 467 3³ × 107 2⁴ × 5 × 23 2 × 17 × 53 2 × 3 × 5² × 11 5 × 7 × 59 2² × 281 2⁴ × 3³ × 5 2 × 3 × 5 × 73 2² × 5² × 11 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 76
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 180 and 200 HCF and LCM of 27 and 90 HCF and LCM of 45 and 81 HCF and LCM of 170 and 187 HCF and LCM of 26 and 195 HCF and LCM of 20 and 28 HCF and LCM of 60 and 70 HCF and LCM of 40 and 220
✅ Answer key — HCF and LCM
HCF = 20, LCM = 1800 HCF = 9, LCM = 270 HCF = 9, LCM = 405 HCF = 17, LCM = 1870 HCF = 13, LCM = 390 HCF = 4, LCM = 140 HCF = 10, LCM = 420 HCF = 20, LCM = 440 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 76
Name: Date: Score: / 8
Find the HCF.
HCF of 672 and 276 (Euclid’s division algorithm) HCF of 682 and 616 (Euclid’s division algorithm) HCF of 697 and 170 (Euclid’s division algorithm) HCF of 602 and 518 (Euclid’s division algorithm) HCF of 225 and 117 (Euclid’s division algorithm) HCF of 880 and 380 (Euclid’s division algorithm) HCF of 608 and 224 (Euclid’s division algorithm) HCF of 312 and 306 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
12 22 17 14 9 20 32 6 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 76
Name: Date: Score: / 6
Solve.
HCF of two numbers is 2 and their LCM is 168. One number is 14. Find the other. HCF of two numbers is 11 and their LCM is 440. One number is 88. Find the other. HCF of two numbers is 8 and their LCM is 448. One number is 64. Find the other. HCF of two numbers is 5 and their LCM is 180. One number is 20. Find the other. HCF of two numbers is 4 and their LCM is 120. One number is 20. Find the other. HCF of two numbers is 6 and their LCM is 126. One number is 42. Find the other.
✅ Answer key — HCF × LCM = product
24 55 56 45 24 18 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 76
Name: Date: Score: / 8
Answer without long division.
Does 65/24 have a terminating decimal expansion? Does 703/1000 have a terminating decimal expansion? Does 791/650 have a terminating decimal expansion? Does 51/20 have a terminating decimal expansion? Does 249/110 have a terminating decimal expansion? Does 205/104 have a terminating decimal expansion? Does 127/50 have a terminating decimal expansion? Does 1529/1500 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2³ × 5³) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2² × 5) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2 × 5²) No — non-terminating repeating (denominator has the factor 3) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 76
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √27 Rational or irrational: √16 Rational or irrational: 3√71 Rational or irrational: 4 + √15 Rational or irrational: 3 + √21 Rational or irrational: 1 + √75 Rational or irrational: 6√25 Rational or irrational: 6 + √96 Rational or irrational: 5 + √52 Rational or irrational: 5 + √49 Rational or irrational: 2 + √75 Rational or irrational: 7√16
✅ Answer key — Rational or irrational?
irrational rational irrational irrational irrational irrational rational irrational irrational rational irrational rational 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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