Match List-I with List-II.
| List-I (Number) | List-II (Number of factors) | ||
|---|---|---|---|
| (A) | 12 | (I) | 8 |
| (B) | 16 | (II) | 3 |
| (C) | 30 | (III) | 6 |
| (D) | 49 | (IV) | 5 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
Write the number as a product of primes \(p^a\times q^b\times\dots\); the number of factors is \((a+1)(b+1)\dots\)
(A) 12 — this matches (III) 6. \(12=2^2\times3\), so it has \((2+1)(1+1)=6\) factors: 1, 2, 3, 4, 6, 12.
(B) 16 — this matches (IV) 5. \(16=2^4\), so it has \(4+1=5\) factors: 1, 2, 4, 8, 16.
(C) 30 — this matches (I) 8. \(30=2\times3\times5\), so it has \(2\times2\times2=8\) factors: 1, 2, 3, 5, 6, 10, 15, 30.
(D) 49 — this matches (II) 3. \(49=7^2\), so it has \(2+1=3\) factors: 1, 7, 49.