Free · Class 10 · 6 worksheets · answer keys · practise online · set 32
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 32
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 918 Prime factorisation of 2256 Prime factorisation of 2664 Prime factorisation of 2652 Prime factorisation of 1910 Prime factorisation of 2565 Prime factorisation of 351 Prime factorisation of 2376 Prime factorisation of 702 Prime factorisation of 1440
✅ Answer key — Prime factorisation
2 × 3³ × 17 2⁴ × 3 × 47 2³ × 3² × 37 2² × 3 × 13 × 17 2 × 5 × 191 3³ × 5 × 19 3³ × 13 2³ × 3³ × 11 2 × 3³ × 13 2⁵ × 3² × 5 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 32
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 56 and 72 HCF and LCM of 114 and 133 HCF and LCM of 54 and 234 HCF and LCM of 80 and 90 HCF and LCM of 36 and 56 HCF and LCM of 55 and 88 HCF and LCM of 117 and 169 HCF and LCM of 30 and 75
✅ Answer key — HCF and LCM
HCF = 8, LCM = 504 HCF = 19, LCM = 798 HCF = 18, LCM = 702 HCF = 10, LCM = 720 HCF = 4, LCM = 504 HCF = 11, LCM = 440 HCF = 13, LCM = 1521 HCF = 15, LCM = 150 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 32
Name: Date: Score: / 8
Find the HCF.
HCF of 315 and 203 (Euclid’s division algorithm) HCF of 413 and 175 (Euclid’s division algorithm) HCF of 969 and 748 (Euclid’s division algorithm) HCF of 530 and 160 (Euclid’s division algorithm) HCF of 456 and 344 (Euclid’s division algorithm) HCF of 656 and 528 (Euclid’s division algorithm) HCF of 975 and 624 (Euclid’s division algorithm) HCF of 637 and 286 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
7 7 17 10 8 16 39 13 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 32
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 180. One number is 45. Find the other. HCF of two numbers is 14 and their LCM is 1176. One number is 98. Find the other. HCF of two numbers is 4 and their LCM is 132. One number is 44. Find the other. HCF of two numbers is 11 and their LCM is 242. One number is 121. Find the other. HCF of two numbers is 11 and their LCM is 605. One number is 55. Find the other. HCF of two numbers is 13 and their LCM is 910. One number is 91. Find the other.
✅ Answer key — HCF × LCM = product
36 168 12 22 121 130 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 32
Name: Date: Score: / 8
Answer without long division.
Does 13/6 have a terminating decimal expansion? Does 7/5 have a terminating decimal expansion? Does 281/110 have a terminating decimal expansion? Does 4/5 have a terminating decimal expansion? Does 5/2 have a terminating decimal expansion? Does 137/140 have a terminating decimal expansion? Does 3341/1400 have a terminating decimal expansion? Does 21/10 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5) Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2 × 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 32
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √42 Rational or irrational: 2√91 Rational or irrational: √82 Rational or irrational: √29 Rational or irrational: 7 + √48 Rational or irrational: 5√90 Rational or irrational: 1√88 Rational or irrational: √53 Rational or irrational: √99 Rational or irrational: 3 + √99 Rational or irrational: 7 + √96 Rational or irrational: √10
✅ 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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