Free · Class 10 · 6 worksheets · answer keys · practise online · set 67
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 67
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1216 Prime factorisation of 1048 Prime factorisation of 136 Prime factorisation of 390 Prime factorisation of 465 Prime factorisation of 513 Prime factorisation of 2853 Prime factorisation of 256 Prime factorisation of 120 Prime factorisation of 1500
✅ Answer key — Prime factorisation
2⁶ × 19 2³ × 131 2³ × 17 2 × 3 × 5 × 13 3 × 5 × 31 3³ × 19 3² × 317 2⁸ 2³ × 3 × 5 2² × 3 × 5³ TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 67
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 28 and 36 HCF and LCM of 55 and 70 HCF and LCM of 32 and 104 HCF and LCM of 78 and 90 HCF and LCM of 180 and 260 HCF and LCM of 36 and 44 HCF and LCM of 171 and 247 HCF and LCM of 81 and 117
✅ Answer key — HCF and LCM
HCF = 4, LCM = 252 HCF = 5, LCM = 770 HCF = 8, LCM = 416 HCF = 6, LCM = 1170 HCF = 20, LCM = 2340 HCF = 4, LCM = 396 HCF = 19, LCM = 2223 HCF = 9, LCM = 1053 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 67
Name: Date: Score: / 8
Find the HCF.
HCF of 992 and 864 (Euclid’s division algorithm) HCF of 992 and 608 (Euclid’s division algorithm) HCF of 418 and 330 (Euclid’s division algorithm) HCF of 882 and 288 (Euclid’s division algorithm) HCF of 884 and 390 (Euclid’s division algorithm) HCF of 902 and 682 (Euclid’s division algorithm) HCF of 420 and 182 (Euclid’s division algorithm) HCF of 630 and 165 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
32 32 22 18 26 22 14 15 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 67
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 594. One number is 54. Find the other. HCF of two numbers is 3 and their LCM is 165. One number is 15. Find the other. HCF of two numbers is 14 and their LCM is 504. One number is 56. Find the other. HCF of two numbers is 9 and their LCM is 504. One number is 72. Find the other. HCF of two numbers is 2 and their LCM is 198. One number is 18. Find the other. HCF of two numbers is 9 and their LCM is 108. One number is 27. Find the other.
✅ Answer key — HCF × LCM = product
99 33 126 63 22 36 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 67
Name: Date: Score: / 8
Answer without long division.
Does 92/625 have a terminating decimal expansion? Does 2709/1000 have a terminating decimal expansion? Does 1/10 have a terminating decimal expansion? Does 43/200 have a terminating decimal expansion? Does 157/100 have a terminating decimal expansion? Does 107/120 have a terminating decimal expansion? Does 317/250 have a terminating decimal expansion? Does 4/35 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5⁴) Yes — terminating (denominator 2³ × 5³) Yes — terminating (denominator 2 × 5) Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 2² × 5²) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2 × 5³) 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 67
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √25 Rational or irrational: 6√91 Rational or irrational: √65 Rational or irrational: √45 Rational or irrational: √56 Rational or irrational: √29 Rational or irrational: 1 + √79 Rational or irrational: 3 + √37 Rational or irrational: 3 + √27 Rational or irrational: √73 Rational or irrational: 1 + √12 Rational or irrational: 7√88
✅ 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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