Free · Class 10 · 6 worksheets · answer keys · practise online · set 74
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 74
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1816 Prime factorisation of 651 Prime factorisation of 1420 Prime factorisation of 2313 Prime factorisation of 472 Prime factorisation of 1521 Prime factorisation of 1170 Prime factorisation of 2751 Prime factorisation of 2667 Prime factorisation of 162
✅ Answer key — Prime factorisation
2³ × 227 3 × 7 × 31 2² × 5 × 71 3² × 257 2³ × 59 3² × 13² 2 × 3² × 5 × 13 3 × 7 × 131 3 × 7 × 127 2 × 3⁴ TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 74
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 190 and 209 HCF and LCM of 45 and 165 HCF and LCM of 40 and 112 HCF and LCM of 96 and 112 HCF and LCM of 24 and 64 HCF and LCM of 39 and 52 HCF and LCM of 195 and 225 HCF and LCM of 108 and 234
✅ Answer key — HCF and LCM
HCF = 19, LCM = 2090 HCF = 15, LCM = 495 HCF = 8, LCM = 560 HCF = 16, LCM = 672 HCF = 8, LCM = 192 HCF = 13, LCM = 156 HCF = 15, LCM = 2925 HCF = 18, LCM = 1404 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 74
Name: Date: Score: / 8
Find the HCF.
HCF of 364 and 169 (Euclid’s division algorithm) HCF of 423 and 261 (Euclid’s division algorithm) HCF of 690 and 465 (Euclid’s division algorithm) HCF of 960 and 456 (Euclid’s division algorithm) HCF of 200 and 144 (Euclid’s division algorithm) HCF of 374 and 110 (Euclid’s division algorithm) HCF of 180 and 130 (Euclid’s division algorithm) HCF of 342 and 270 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
13 9 15 24 8 22 10 18 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 74
Name: Date: Score: / 6
Solve.
HCF of two numbers is 11 and their LCM is 616. One number is 77. Find the other. HCF of two numbers is 2 and their LCM is 90. One number is 18. Find the other. HCF of two numbers is 12 and their LCM is 792. One number is 132. Find the other. HCF of two numbers is 9 and their LCM is 594. One number is 99. Find the other. HCF of two numbers is 4 and their LCM is 84. One number is 12. Find the other. HCF of two numbers is 2 and their LCM is 264. One number is 24. Find the other.
✅ Answer key — HCF × LCM = product
88 10 72 54 28 22 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 74
Name: Date: Score: / 8
Answer without long division.
Does 19/120 have a terminating decimal expansion? Does 1421/1000 have a terminating decimal expansion? Does 2/25 have a terminating decimal expansion? Does 285/112 have a terminating decimal expansion? Does 27/16 have a terminating decimal expansion? Does 3/5 have a terminating decimal expansion? Does 2457/1250 have a terminating decimal expansion? Does 239/400 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2³ × 5³) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 5) Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 2⁴ × 5²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 74
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √78 Rational or irrational: √28 Rational or irrational: √86 Rational or irrational: 2 + √23 Rational or irrational: 5√74 Rational or irrational: 5√97 Rational or irrational: 2 + √97 Rational or irrational: 5 + √38 Rational or irrational: 6√95 Rational or irrational: 5 + √34 Rational or irrational: √19 Rational or irrational: 3 + √18
✅ 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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