Free · Class 10 · 6 worksheets · answer keys · practise online · set 89
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 89
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1788 Prime factorisation of 438 Prime factorisation of 2937 Prime factorisation of 1776 Prime factorisation of 322 Prime factorisation of 975 Prime factorisation of 1192 Prime factorisation of 2910 Prime factorisation of 2726 Prime factorisation of 1875
✅ Answer key — Prime factorisation
2² × 3 × 149 2 × 3 × 73 3 × 11 × 89 2⁴ × 3 × 37 2 × 7 × 23 3 × 5² × 13 2³ × 149 2 × 3 × 5 × 97 2 × 29 × 47 3 × 5⁴ TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 89
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 54 and 63 HCF and LCM of 15 and 50 HCF and LCM of 182 and 210 HCF and LCM of 220 and 300 HCF and LCM of 247 and 266 HCF and LCM of 18 and 42 HCF and LCM of 18 and 33 HCF and LCM of 40 and 140
✅ Answer key — HCF and LCM
HCF = 9, LCM = 378 HCF = 5, LCM = 150 HCF = 14, LCM = 2730 HCF = 20, LCM = 3300 HCF = 19, LCM = 3458 HCF = 6, LCM = 126 HCF = 3, LCM = 198 HCF = 20, LCM = 280 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 89
Name: Date: Score: / 8
Find the HCF.
HCF of 236 and 144 (Euclid’s division algorithm) HCF of 518 and 168 (Euclid’s division algorithm) HCF of 832 and 234 (Euclid’s division algorithm) HCF of 931 and 209 (Euclid’s division algorithm) HCF of 456 and 204 (Euclid’s division algorithm) HCF of 391 and 221 (Euclid’s division algorithm) HCF of 207 and 144 (Euclid’s division algorithm) HCF of 481 and 156 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
4 14 26 19 12 17 9 13 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 89
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 405. One number is 81. Find the other. HCF of two numbers is 12 and their LCM is 504. One number is 84. Find the other. HCF of two numbers is 9 and their LCM is 990. One number is 99. Find the other. HCF of two numbers is 3 and their LCM is 60. One number is 12. Find the other. HCF of two numbers is 8 and their LCM is 224. One number is 32. Find the other. HCF of two numbers is 2 and their LCM is 84. One number is 12. Find the other.
✅ Answer key — HCF × LCM = product
45 72 90 15 56 14 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 89
Name: Date: Score: / 8
Answer without long division.
Does 1149/560 have a terminating decimal expansion? Does 1/8 have a terminating decimal expansion? Does 689/400 have a terminating decimal expansion? Does 7/6 have a terminating decimal expansion? Does 93/200 have a terminating decimal expansion? Does 108/65 have a terminating decimal expansion? Does 21/125 have a terminating decimal expansion? Does 29/52 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2³) Yes — terminating (denominator 2⁴ × 5²) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2³ × 5²) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 13) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 89
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 9 + √97 Rational or irrational: 5√67 Rational or irrational: 5√74 Rational or irrational: √59 Rational or irrational: 6 + √89 Rational or irrational: 8 + √14 Rational or irrational: 8 + √97 Rational or irrational: √62 Rational or irrational: √73 Rational or irrational: 8 + √91 Rational or irrational: 8√49 Rational or irrational: 8 + √33
✅ 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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