Free · Class 10 · 6 worksheets · answer keys · practise online · set 17
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 17
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1568 Prime factorisation of 931 Prime factorisation of 2886 Prime factorisation of 1425 Prime factorisation of 693 Prime factorisation of 2224 Prime factorisation of 1786 Prime factorisation of 325 Prime factorisation of 1626 Prime factorisation of 1274
✅ Answer key — Prime factorisation
2⁵ × 7² 7² × 19 2 × 3 × 13 × 37 3 × 5² × 19 3² × 7 × 11 2⁴ × 139 2 × 19 × 47 5² × 13 2 × 3 × 271 2 × 7² × 13 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 17
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 192 and 208 HCF and LCM of 48 and 56 HCF and LCM of 26 and 117 HCF and LCM of 72 and 78 HCF and LCM of 32 and 208 HCF and LCM of 182 and 196 HCF and LCM of 22 and 55 HCF and LCM of 55 and 70
✅ Answer key — HCF and LCM
HCF = 16, LCM = 2496 HCF = 8, LCM = 336 HCF = 13, LCM = 234 HCF = 6, LCM = 936 HCF = 16, LCM = 416 HCF = 14, LCM = 2548 HCF = 11, LCM = 110 HCF = 5, LCM = 770 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 17
Name: Date: Score: / 8
Find the HCF.
HCF of 132 and 100 (Euclid’s division algorithm) HCF of 405 and 369 (Euclid’s division algorithm) HCF of 540 and 410 (Euclid’s division algorithm) HCF of 507 and 156 (Euclid’s division algorithm) HCF of 360 and 336 (Euclid’s division algorithm) HCF of 602 and 350 (Euclid’s division algorithm) HCF of 583 and 495 (Euclid’s division algorithm) HCF of 920 and 560 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
4 9 10 39 24 14 11 40 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 17
Name: Date: Score: / 6
Solve.
HCF of two numbers is 8 and their LCM is 288. One number is 72. Find the other. HCF of two numbers is 6 and their LCM is 198. One number is 66. Find the other. HCF of two numbers is 2 and their LCM is 84. One number is 14. Find the other. HCF of two numbers is 10 and their LCM is 240. One number is 80. Find the other. HCF of two numbers is 9 and their LCM is 126. One number is 18. Find the other. HCF of two numbers is 6 and their LCM is 792. One number is 72. Find the other.
✅ Answer key — HCF × LCM = product
32 18 12 30 63 66 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 17
Name: Date: Score: / 8
Answer without long division.
Does 11/12 have a terminating decimal expansion? Does 1991/1250 have a terminating decimal expansion? Does 28/15 have a terminating decimal expansion? Does 5883/2000 have a terminating decimal expansion? Does 3982/1875 have a terminating decimal expansion? Does 231/100 have a terminating decimal expansion? Does 19/14 have a terminating decimal expansion? Does 63/26 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2 × 5⁴) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2⁴ × 5³) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2² × 5²) No — non-terminating repeating (denominator has the factor 7) 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 17
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 8√95 Rational or irrational: √100 Rational or irrational: 1 + √48 Rational or irrational: 2√65 Rational or irrational: √74 Rational or irrational: 1√60 Rational or irrational: 7 + √66 Rational or irrational: 8√13 Rational or irrational: √75 Rational or irrational: √14 Rational or irrational: √98 Rational or irrational: 2√86
✅ Answer key — Rational or irrational?
irrational rational 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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