All Exams: Mathematics — Number System Practice MCQs (2026)

Practise these 20 carefully crafted MCQs on Number System designed for All Exams 2026. Each question carries a detailed explanation to reinforce learning.

Q1. LCM of 12, 18 and 24?

  • A) 36
  • B) 48
  • C) 72
  • D) 96
Answer: C) 72 — 72 = 2³×3².

Q2. HCF of 48 and 180?

  • A) 6
  • B) 12
  • C) 18
  • D) 24
Answer: B) 12 — 48=2⁴×3; 180=2²×3²×5. HCF=2²×3=12.

Q3. Which is NOT a prime number?

  • A) 2
  • B) 17
  • C) 19
  • D) 21
Answer: D) 21 — 21=3×7, not prime.

Q4. Sum of digits of 9999?

  • A) 27
  • B) 33
  • C) 36
  • D) 42
Answer: C) 36 — 9+9+9+9=36.

Q5. Find the unit digit of 3⁴⁷?

  • A) 1
  • B) 3
  • C) 7
  • D) 9
Answer: C) 7 — Cycle of 4: 3¹=3,3²=9,3³=27(7),3⁴=81(1). 47 mod 4=3 → unit digit=7.

Q6. Remainder when 17²³ is divided by 16?

  • A) 1
  • B) 3
  • C) 7
  • D) 15
Answer: A) 1 — 17≡1(mod16) → 17²³≡1.

Q7. Find value: sum of 1 to 100?

  • A) 4050
  • B) 4500
  • C) 5050
  • D) 5500
Answer: C) 5050 — 100×101/2=5050.

Q8. Which is divisible by both 9 and 11?

  • A) 891
  • B) 990
  • C) 1001
  • D) 1089
Answer: B) 990 — 990/9=110; 990/11=90. Both divide evenly.

Q9. Simplify: 2⁵×2³÷2⁴

  • A) 16
  • B) 32
  • C) 64
  • D) 128
Answer: A) 16 — 2^(5+3-4)=2⁴=16.

Q10. Sum of first 50 odd numbers?

  • A) 2000
  • B) 2500
  • C) 3025
  • D) 3600
Answer: B) 2500 — n²=50²=2500.

Q11. Which is divisible by 8?

  • A) 1064
  • B) 1070
  • C) 1076
  • D) 1080
Answer: D) 1080 — 1080/8=135.

Q12. Number of primes between 1 and 50?

  • A) 13
  • B) 15
  • C) 16
  • D) 17
Answer: B) 15 — 15 primes: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47.

Q13. Find missing: 7, 13, 21, 31, ?

  • A) 41
  • B) 42
  • C) 43
  • D) 45
Answer: C) 43 — Differences 6,8,10,12 → next=43.

Q14. Largest 5-digit number divisible by 37?

  • A) 99902
  • B) 99936
  • C) 99974
  • D) 99999
Answer: A) 99902 — 99999÷37=2702.67; 2702×37=99974.

Q15. √1024?

  • A) 28
  • B) 30
  • C) 32
  • D) 36
Answer: C) 32 — 32²=1024.

Q16. If n is odd, which is always even?

  • A) n+1
  • B) n²+n
  • C) n²
  • D) n-1
Answer: B) n²+n — n²+n=n(n+1) — product of consecutive integers.

Q17. 5! - 4!?

  • A) 72
  • B) 96
  • C) 100
  • D) 110
Answer: B) 96 — 120-24=96.

Q18. LCM of fractions 2/3, 4/9, 8/27?

  • A) 8/3
  • B) 4/3
  • C) 8/9
  • D) 2/3
Answer: A) 8/3 — LCM(2,4,8)/HCF(3,9,27)=8/3.

Q19. Co-prime pair?

  • A) (4,6)
  • B) (8,12)
  • C) (9,27)
  • D) (14,15)
Answer: D) (14,15) — HCF(14,15)=1.

Q20. Which number has exactly 3 factors?

  • A) 8
  • B) 9
  • C) 12
  • D) 15
Answer: B) 9 — 9=3²; factors: 1,3,9 — exactly 3.