Free · Class 10 · 6 worksheets · answer keys · practise online · set 40
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 40
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2652 Prime factorisation of 426 Prime factorisation of 658 Prime factorisation of 1449 Prime factorisation of 1550 Prime factorisation of 1048 Prime factorisation of 2829 Prime factorisation of 2340 Prime factorisation of 2812 Prime factorisation of 1112
✅ Answer key — Prime factorisation
2² × 3 × 13 × 17 2 × 3 × 71 2 × 7 × 47 3² × 7 × 23 2 × 5² × 31 2³ × 131 3 × 23 × 41 2² × 3² × 5 × 13 2² × 19 × 37 2³ × 139 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 40
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 99 and 143 HCF and LCM of 30 and 36 HCF and LCM of 91 and 105 HCF and LCM of 196 and 210 HCF and LCM of 72 and 80 HCF and LCM of 54 and 78 HCF and LCM of 88 and 96 HCF and LCM of 12 and 15
✅ Answer key — HCF and LCM
HCF = 11, LCM = 1287 HCF = 6, LCM = 180 HCF = 7, LCM = 1365 HCF = 14, LCM = 2940 HCF = 8, LCM = 720 HCF = 6, LCM = 702 HCF = 8, LCM = 1056 HCF = 3, LCM = 60 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 40
Name: Date: Score: / 8
Find the HCF.
HCF of 775 and 575 (Euclid’s division algorithm) HCF of 774 and 432 (Euclid’s division algorithm) HCF of 425 and 204 (Euclid’s division algorithm) HCF of 611 and 429 (Euclid’s division algorithm) HCF of 363 and 231 (Euclid’s division algorithm) HCF of 376 and 240 (Euclid’s division algorithm) HCF of 472 and 144 (Euclid’s division algorithm) HCF of 405 and 297 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
25 18 17 13 33 8 8 27 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 40
Name: Date: Score: / 6
Solve.
HCF of two numbers is 13 and their LCM is 715. One number is 65. Find the other. HCF of two numbers is 11 and their LCM is 330. One number is 110. Find the other. HCF of two numbers is 11 and their LCM is 440. One number is 55. Find the other. HCF of two numbers is 7 and their LCM is 210. One number is 70. Find the other. HCF of two numbers is 15 and their LCM is 1320. One number is 120. Find the other. HCF of two numbers is 8 and their LCM is 448. One number is 56. Find the other.
✅ Answer key — HCF × LCM = product
143 33 88 21 165 64 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 40
Name: Date: Score: / 8
Answer without long division.
Does 129/50 have a terminating decimal expansion? Does 59/50 have a terminating decimal expansion? Does 57/176 have a terminating decimal expansion? Does 2247/1000 have a terminating decimal expansion? Does 1123/500 have a terminating decimal expansion? Does 211/112 have a terminating decimal expansion? Does 3/4 have a terminating decimal expansion? Does 683/600 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2 × 5²) Yes — terminating (denominator 2 × 5²) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2³ × 5³) Yes — terminating (denominator 2² × 5³) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2²) No — non-terminating repeating (denominator has the factor 3) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 40
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √60 Rational or irrational: 5√12 Rational or irrational: 2√47 Rational or irrational: 1 + √40 Rational or irrational: √55 Rational or irrational: 9√32 Rational or irrational: 9 + √10 Rational or irrational: 5 + √41 Rational or irrational: 5 + √60 Rational or irrational: 9√19 Rational or irrational: √32 Rational or irrational: 2√63
✅ 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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