Free · Class 10 · 6 worksheets · answer keys · practise online · set 65
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 65
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2910 Prime factorisation of 2185 Prime factorisation of 1430 Prime factorisation of 850 Prime factorisation of 627 Prime factorisation of 1445 Prime factorisation of 1072 Prime factorisation of 1054 Prime factorisation of 2514 Prime factorisation of 1280
✅ Answer key — Prime factorisation
2 × 3 × 5 × 97 5 × 19 × 23 2 × 5 × 11 × 13 2 × 5² × 17 3 × 11 × 19 5 × 17² 2⁴ × 67 2 × 17 × 31 2 × 3 × 419 2⁸ × 5 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 65
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 30 and 100 HCF and LCM of 99 and 143 HCF and LCM of 65 and 117 HCF and LCM of 104 and 120 HCF and LCM of 135 and 210 HCF and LCM of 25 and 55 HCF and LCM of 160 and 208 HCF and LCM of 28 and 77
✅ Answer key — HCF and LCM
HCF = 10, LCM = 300 HCF = 11, LCM = 1287 HCF = 13, LCM = 585 HCF = 8, LCM = 1560 HCF = 15, LCM = 1890 HCF = 5, LCM = 275 HCF = 16, LCM = 2080 HCF = 7, LCM = 308 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 65
Name: Date: Score: / 8
Find the HCF.
HCF of 400 and 360 (Euclid’s division algorithm) HCF of 500 and 480 (Euclid’s division algorithm) HCF of 400 and 390 (Euclid’s division algorithm) HCF of 989 and 759 (Euclid’s division algorithm) HCF of 777 and 588 (Euclid’s division algorithm) HCF of 736 and 208 (Euclid’s division algorithm) HCF of 672 and 651 (Euclid’s division algorithm) HCF of 696 and 408 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
40 20 10 23 21 16 21 24 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 65
Name: Date: Score: / 6
Solve.
HCF of two numbers is 3 and their LCM is 90. One number is 18. Find the other. HCF of two numbers is 15 and their LCM is 315. One number is 105. Find the other. HCF of two numbers is 14 and their LCM is 210. One number is 42. Find the other. HCF of two numbers is 5 and their LCM is 220. One number is 55. Find the other. HCF of two numbers is 11 and their LCM is 264. One number is 88. Find the other. HCF of two numbers is 15 and their LCM is 1650. One number is 150. Find the other.
✅ Answer key — HCF × LCM = product
15 45 70 20 33 165 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 65
Name: Date: Score: / 8
Answer without long division.
Does 59/100 have a terminating decimal expansion? Does 761/1040 have a terminating decimal expansion? Does 9/5 have a terminating decimal expansion? Does 1723/2000 have a terminating decimal expansion? Does 2997/1250 have a terminating decimal expansion? Does 1/2 have a terminating decimal expansion? Does 107/130 have a terminating decimal expansion? Does 13/14 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2² × 5²) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5) Yes — terminating (denominator 2⁴ × 5³) Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 13) 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 65
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 7√56 Rational or irrational: 3 + √90 Rational or irrational: √55 Rational or irrational: √63 Rational or irrational: √59 Rational or irrational: 5 + √35 Rational or irrational: 4 + √5 Rational or irrational: √60 Rational or irrational: 6√96 Rational or irrational: 1√11 Rational or irrational: √9 Rational or irrational: √11
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational irrational irrational irrational rational 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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