Free · Class 10 · 6 worksheets · answer keys · practise online · set 84
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 84
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1842 Prime factorisation of 2650 Prime factorisation of 1970 Prime factorisation of 2706 Prime factorisation of 578 Prime factorisation of 2292 Prime factorisation of 315 Prime factorisation of 1265 Prime factorisation of 352 Prime factorisation of 2241
✅ Answer key — Prime factorisation
2 × 3 × 307 2 × 5² × 53 2 × 5 × 197 2 × 3 × 11 × 41 2 × 17² 2² × 3 × 191 3² × 5 × 7 5 × 11 × 23 2⁵ × 11 3³ × 83 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 84
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 84 and 144 HCF and LCM of 220 and 280 HCF and LCM of 104 and 169 HCF and LCM of 45 and 150 HCF and LCM of 56 and 105 HCF and LCM of 32 and 120 HCF and LCM of 18 and 78 HCF and LCM of 98 and 154
✅ Answer key — HCF and LCM
HCF = 12, LCM = 1008 HCF = 20, LCM = 3080 HCF = 13, LCM = 1352 HCF = 15, LCM = 450 HCF = 7, LCM = 840 HCF = 8, LCM = 480 HCF = 6, LCM = 234 HCF = 14, LCM = 1078 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 84
Name: Date: Score: / 8
Find the HCF.
HCF of 884 and 561 (Euclid’s division algorithm) HCF of 957 and 594 (Euclid’s division algorithm) HCF of 153 and 111 (Euclid’s division algorithm) HCF of 416 and 328 (Euclid’s division algorithm) HCF of 630 and 483 (Euclid’s division algorithm) HCF of 774 and 540 (Euclid’s division algorithm) HCF of 816 and 504 (Euclid’s division algorithm) HCF of 196 and 112 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
17 33 3 8 21 18 24 28 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 84
Name: Date: Score: / 6
Solve.
HCF of two numbers is 10 and their LCM is 400. One number is 50. Find the other. HCF of two numbers is 7 and their LCM is 126. One number is 14. Find the other. HCF of two numbers is 5 and their LCM is 280. One number is 40. Find the other. HCF of two numbers is 14 and their LCM is 980. One number is 98. Find the other. HCF of two numbers is 15 and their LCM is 420. One number is 105. Find the other. HCF of two numbers is 3 and their LCM is 198. One number is 33. Find the other.
✅ Answer key — HCF × LCM = product
80 63 35 140 60 18 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 84
Name: Date: Score: / 8
Answer without long division.
Does 1/48 have a terminating decimal expansion? Does 26/25 have a terminating decimal expansion? Does 33/80 have a terminating decimal expansion? Does 373/250 have a terminating decimal expansion? Does 23/40 have a terminating decimal expansion? Does 113/130 have a terminating decimal expansion? Does 73/40 have a terminating decimal expansion? Does 211/175 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5²) Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 2 × 5³) Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 7) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 84
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 6√64 Rational or irrational: √33 Rational or irrational: 8 + √72 Rational or irrational: 8√41 Rational or irrational: √10 Rational or irrational: 8 + √19 Rational or irrational: √60 Rational or irrational: 6 + √80 Rational or irrational: 4√97 Rational or irrational: √61 Rational or irrational: 2√27 Rational or irrational: √11
✅ Answer key — Rational or irrational?
rational 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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