Examination Questions in HCF and LCM
1. What is the HCF of 8(x 5 - x 3 + x) and 28(x 6 + 1)?
- 4(x 4 - x 2 + 1)
- 2(x 4 - x 2 + 1)
- (x 4 - x 2 + 1)
- None of the above
2. What is the number of integral solutions of the equations HCF (a, b) = 5 and a + b = 65?
- None
- Infinitely many
- Less than 65
- Exactly one
3. For any integers ‘a’ and ‘b’ with HCF (a, b) = 1, what is HCF (a + b, a – b) equal to?
- It is always 1
- It is always 2
- Either 1 or 2
- None of the above
4. The HCF of two numbers is 98 and their LCM is 2352. The sum of the numbers may be
- 1372
- 1398
- 1426
- 1484
5. What is the HCF of a 2 b 4 + 2a 2 b 2 and (ab) 7 – 4a 2 b 9?
- ab
- a 2 b2
- a 2 b2
- a 3 b2
6. What is the LCM of x 2 +2x – 8, x 3 - 4x 2 + 4x and x 2 + 4x?
- x(x + 4)(x – 2) 2
- x(x + 4)(x – 2)
- x(x + 4)(x + 2) 2
- x(x + 4) 2(x – 2)
7. For integers a, b and c, if HCF(a, b) = 1 and HCF(a, c) = 1, then which one of the following is correct?
- HCF(a, bc) = 1
- HCF(a, bc) = a
- HCF(a, bc) = b
- None of the above
8. For any integer n, what is the HCF of integers m = 2n + 1 and k = 9n + 4?
- 3
- 1
- 2
- 4
9. If (x – 6) is the HCF of x 2 – 2x – 24 and x 2 – kx – 6, then what is the value of k?
- 3
- 5
- 6
- 8
10. What is the HCF of 36(3x4 + 5x3 – 2x2), 9(6x3 + 4x2 – 2x), 54(27x4 – x)?
- 9x(x + 1)
- 9x(3x – 1)
- 18x(3x – 1)
- 18x(x + 1)
11. Consider the following statements :
- The HCF of x + y and x10 – y10 is x + y.
- The HCF of x + y and x10 + y10 is x + y.
- The HCF of x – y and x10 + y10 is x – y.
- The HCF of x – y and x10 – y10 is x – y.
Which of the statements given above are correct?
- 1 and 2
- 2 and 3
- 1 and 4
- 2 and 4
12. What is the HCF of the polynomials x 4 – 3x + 2, x 3 – 3x 2 + 3x – 1 and x 4 – 1?
- x – 1
- x + 1
- x2 – 1
- None of the above