Free · Class 10 · 6 worksheets · answer keys · practise online · set 57
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 57
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 808 Prime factorisation of 2112 Prime factorisation of 2094 Prime factorisation of 861 Prime factorisation of 1588 Prime factorisation of 2456 Prime factorisation of 2828 Prime factorisation of 1173 Prime factorisation of 1800 Prime factorisation of 772
✅ Answer key — Prime factorisation
2³ × 101 2⁶ × 3 × 11 2 × 3 × 349 3 × 7 × 41 2² × 397 2³ × 307 2² × 7 × 101 3 × 17 × 23 2³ × 3² × 5² 2² × 193 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 57
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 60 and 105 HCF and LCM of 15 and 33 HCF and LCM of 50 and 90 HCF and LCM of 221 and 255 HCF and LCM of 35 and 56 HCF and LCM of 15 and 36 HCF and LCM of 15 and 50 HCF and LCM of 72 and 99
✅ Answer key — HCF and LCM
HCF = 15, LCM = 420 HCF = 3, LCM = 165 HCF = 10, LCM = 450 HCF = 17, LCM = 3315 HCF = 7, LCM = 280 HCF = 3, LCM = 180 HCF = 5, LCM = 150 HCF = 9, LCM = 792 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 57
Name: Date: Score: / 8
Find the HCF.
HCF of 900 and 522 (Euclid’s division algorithm) HCF of 259 and 238 (Euclid’s division algorithm) HCF of 500 and 330 (Euclid’s division algorithm) HCF of 560 and 525 (Euclid’s division algorithm) HCF of 612 and 594 (Euclid’s division algorithm) HCF of 624 and 516 (Euclid’s division algorithm) HCF of 413 and 189 (Euclid’s division algorithm) HCF of 768 and 600 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
18 7 10 35 18 12 7 24 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 57
Name: Date: Score: / 6
Solve.
HCF of two numbers is 8 and their LCM is 192. One number is 64. Find the other. HCF of two numbers is 13 and their LCM is 520. One number is 65. Find the other. HCF of two numbers is 11 and their LCM is 165. One number is 33. Find the other. HCF of two numbers is 6 and their LCM is 180. One number is 30. Find the other. HCF of two numbers is 14 and their LCM is 1078. One number is 98. Find the other. HCF of two numbers is 12 and their LCM is 396. One number is 36. Find the other.
✅ Answer key — HCF × LCM = product
24 104 55 36 154 132 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 57
Name: Date: Score: / 8
Answer without long division.
Does 214/625 have a terminating decimal expansion? Does 543/280 have a terminating decimal expansion? Does 3/4 have a terminating decimal expansion? Does 33/28 have a terminating decimal expansion? Does 9/8 have a terminating decimal expansion? Does 841/2000 have a terminating decimal expansion? Does 18/55 have a terminating decimal expansion? Does 7/400 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2²) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2³) Yes — terminating (denominator 2⁴ × 5³) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2⁴ × 5²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 57
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √47 Rational or irrational: √99 Rational or irrational: 2 + √53 Rational or irrational: 4√97 Rational or irrational: 3 + √79 Rational or irrational: √23 Rational or irrational: 7√71 Rational or irrational: 1 + √88 Rational or irrational: 8 + √42 Rational or irrational: √87 Rational or irrational: 1√75 Rational or irrational: 9√97
✅ 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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