Class 7 math chapter 9 factor HCF and LCM
Complete guide to factors, GCD, and LCM for class 7,Class 7 math lesson on GCD and LCM with examples,
Step-by-step guide for finding GCD and LCM in grade 7 math,Factors and multiples explained for 7th grade students,Key concepts of GCD and LCM in class 7 mathematics,Detailed explanations of LCM and GCD in grade 7 math,Math tips and tricks for LCM and GCD – class 7,Solving problems on GCD and LCM for grade 7 math,
In-depth notes on factors, GCD, and LCM for class 7,Practical applications of GCD and LCM in class 7 mathematics
1. Which of the following is the factored form of 5 - 4x - x^2?
(a) (x + 2)(x – 3)
(b) (x + 1)(x – 5)
(c) (x – 1)(x + 5)
√(d) (5 + x)(1 – x)
2. Which of the following is the formula to determine the area of a rectangle?
(a) Length + Width
(b) Length – Width
√(c) Length \times Width
(d) Length \div Width
3. Which of the following are factors or divisors of 12?
i. 1, 2, 3
ii. 4, 6, 12
iii. 3, 6, 9
Which of the following is correct?
√(a) i and iii
(b) ii and iii
(c) i, ii, and iii
(d) i, ii, and iii
4. If a rectangle has an area of 12 square meters and a length of 4 meters, what is its width?
(a) 2 meters
√(b) 3 meters
(c) 4 meters
(d) 12 meters
5. If the length of a rectangle with a width of 3 meters and a length of 4 meters is increased by x meters, what will the new area be?
(a) (4x + 12) square meters
(b) (3x + 4) square meters
√(c) (3x + 12) square meters
(d) (4x + 3) square meters
6. What is the greatest common divisor of 3 and 12?
(a) 1
√(b) 3
(c) 4
(d) 12
7. What are the factors of (3x + 12)?
i. 3
ii. (x + 3)
iii. (x + 4)
Which of the following is correct?
(a) i and ii
(b) ii and iii
√(c) i and iii
(d) i, ii, and iii
8. If the length and width of a rectangle are (3x^2 + 2x + 4) units and 3x^2 units respectively, what is its area?
√(a) 9x^4 + 6x^3 + 12x^2 square units
(b) 9x^3 + 6x^2 + 12x square units
(c) 6x^2 + 9x^3 + 12x^2 square units
(d) 6x^3 + 9x^2 + 12x square units
9. What is the greatest common divisor of 6x^3, 9x^4, and 12x^2?
√(a) 3x^2
(b) 6x^3
(c) 9x^4
(d) 12x
10. What are the factors of 9?
(a) 1, 3, 6
√(b) 1, 3, 9
(c) 1, 6, 9
(d) 3, 6, 9
Observe the following stimulus and answer questions 11 and 12.
11. What are the length and width of the above rectangle?
(a) (x + 1) units and (x + 2) units
(b) (x + 2) units and (x + 3) units
(c) (x + 3) units and (x + 2) units
√(d) (x + 2) units and (x + 1) units
12. The area of the rectangle—
i. (x^2 - 3x + 2) square units
ii. (x^2 + 3x + 2) square units
iii. (x + 1)(x + 2) square units
Which of the following is correct?
(a) i and ii
√(b) ii and iii
(c) i and iii
(d) i, ii, and iii
13. If the area of a rectangle is (x^2 + 5x + 6) square meters and its width is (x + 2) meters, what is its length?
(a) (x + 1) meters
(b) (x + 3) meters
√(c) (x + 4) meters
(d) (x + 5) meters
14. What is the GCD of the expressions 8x^2 yz^2 and 10x^3 y^2 z^4?
(a) 2xyz
√(b) 2x^2 yz^2
(c) 8x^3 yz^2
(d) 40x^3 y^2 z^4
Class 7 Math: Annual exam preparation
15. The product of all common prime factors of two or more expressions is called what?
√(a) GCD
(b) LCM
(c) Common Factor
(d) Least Common Multiple
16. In the expression xy, each of x and y is called—
i. Factor
ii. Multiplier
iii. Multiplicand
Which of the following is correct?
√(a) i and ii
(b) ii and iii
(c) i and iii
(d) i, ii, and iii
17. In xz, what is x or z called?
(a) Factor
(b) Multiplier
√(c) Multiplicand
(d) Divisor
18. What is the common factor of xy and xz?
√(a) x
(b) y
(c) z
(d) xyz
19. What is the GCD of 1, 3, 5?
√(a) 1
(b) 3
(c) 5
(d) 15
20. If the length, width, and height of a box are x meters, y meters, and z meters respectively, what is the volume of the box?
√(a) xyz cubic meters
(b) x^2 yz cubic meters
(c) xyz^2 cubic meters
(d) xy^2 z cubic meters
21. If a box has a volume of xyp and its length and width are x meters and y meters, respectively, what is its height?
(a) xy meters
(b) xp meters
(c) yp meters
√(d) p meters
22. In xyz, what is x, y, or z called?
(a) Multiplier
(b) Multiplicand
√(c) Factor
(d) Divisor
23. What is each of x, y, z called in the expression xyz?
√(a) Multiplier
(b) Multiplicand
(c) Dividend
(d) Remainder
24. What is the common multiple of xyz and xyp?
(a) xy
(b) p
(c) xyp
√(d) xyzp
25. What is the common factor of xyz and xyp?
√(a) xy
(b) xp
(c) yp
(d) zp
26. What is the GCD of 6a^3 b^2 c and 9a^4 b d^2?
(a) 3abcd
(b) 3a^2 b^2 c
√(c) 3a^3 b
(d) 3a^3 b d^2
27. The expression with the lowest degree that is completely divisible by two or more expressions is called the what of those expressions?
√(a) LCM
(b) GCD
(c) Common Factor
(d) Least Common Factor
28. What is the LCM of 2xy and 3xz?
√(a) 6xyz
(b) xy
(c) xz
(d) yx
29. What is the LCM of 6x^2 y and 12x^3 y^2?
(a) 10x^3 y^2
√(b) 12x^3 y^2
(c) 11x^3 y^2
(d) 9x^3 y^2
30. What is the LCM of the expressions xyz, 5x, and 3xp?
(a) xyz
(b) x
(c) 5x
√(d) 15xyzp
31. What is the LCM of 3x^3 y^2 and 2x^2 y^3?
(a) 2x^2 y^2
(b) 3x^2 y^2
(c) 6x^2 y^2
√(d) 6x^3 y^3
32. What is the LCM of 5ab^2 x^2 and 10a^2 b y^2?
(a) 5ab
√(b) 10a^2 b^2 x^2 y^2
(c) 5abxy
(d) 10abx^2 y^2
33. What is the LCM of a^2 - b^2 and a - b?
(a) a^2 + b^2
(b) a^2 \div b^2
√(c) a^2 - b^2
(d) a^2 × b^2
Answer in one word.
Question 1. Write the formula for calculating the area of a rectangle.
Answer: Length \times Width.
Question 2. List the divisors or factors of 12.
Answer: 1, 2, 3, 4, 6, and 12.
Question 3. What is the factor of 3x + 12?
Answer: 3 (x + 4).
Question 4. What do you call a number that can completely divide another number?
Answer: Divisor.
Question 5. What is the greatest common divisor of 6 and 9?
Answer: 3.
Question 6. What is the factor of 20x + 4y?
Answer: 4 (5x + y).
Question 7. What is the factor of 28a + 7b?
Answer: 7(4a + b).
Question 8. What is the greatest common divisor of 6x^3 and 12x^2?
Answer: 3x^2.
Question 9. What is the common factor of 3x^2 and 2x?
Answer: x.
Question 10. What is the factor of 15y - 9y^2?
Answer: 3y (5 - 3y).
Question 11. Write 5a^2 b^2 - 9a b^2 in factored form.
Answer: a^2 b^2 (5 - 9a).
Question 12. List the factors of x^2 + 5x + 6.
Answer: (x + 2) and (x + 3).
Question 13. Write x^2 - x - 2 in factored form.
Answer: (x - 2)(x + 1).
Question 14. Write x^2 - 3x + 2 in factored form.
Answer: (x - 2)(x - 1).
Question 15. Write x^2 - 4x + 4 in factored form.
Answer: (x - 2)(x - 2).
Question 16. Write x^2 - 2x + 1 in factored form.
Answer: (x - 1)(x - 1).
Question 17. If the width of a rectangle is 14xy units and the area is 42xy^3 square units, what is the length?
Answer: Length is 3y^2 units.
Question 18. If the length of a rectangle is (x + 4) meters and its area is x^2 + 7x + 12 square meters, what is the width?
Answer: (x + 3) meters.
Question 19. If the area of a rectangle is 24 square meters and the length is 6 meters, what is the width?
Answer: 4 meters.
Question 20. If the width of a rectangle is 3 meters and the length is 4 meters, and the length is increased by x meters, what will be the new area?
Answer: (3x + 12) square meters.
Question 21. What are the factors of (3x + 12)?
Answer: 3 and (x + 4).
Question 22. What are the factors of 9?
Answer: 1, 3, 9.
Question 23. If a rectangle has an area of (9x^4 + 6x^3 + 12x^2) square units and a width of 3x^2 units, what is its length?
Answer: (3x^2 + 2x + 4) units.
Question 24. What are the factors of 20x + 4y?
Answer: 4 and (5x + y).
Question 25. What is the area of a rectangle with a width of (x + 2) units and a length of (x + 3) units?
Answer: (x^2 + 5x + 6) square units.
Question 26. What are each of x and y called in the expression xy?
Answer: Divisor, factor, or multiplier.
Question 27. What is the GCD of 8x^2 y z^2 and 10x^3 y^2 z^3?
Answer: 2x^2 y z^2.
Question 28. What are each of x, y, p called in the expression xyp?
Answer: Multiplier, factor, or divisor.
Question 29. List the factors of 8.
Answer: 1, 2, 4, 8.
Question 30. List the factors of (3x + 12).
Answer: 3 and (x + 4).
Question 31. List the factors of 6.
Answer: 1, 2, 3, 6.
Question 32. List the factors of x^2 + 7x + 12.
Answer: (x + 4) and (x + 3).
Question 33. What is the common factor of the expressions xy and xz?
Answer: x.
Question 34. What is the full form of GCD?
Answer: Greatest Common Divisor.
Question 35. What is the full form of HCF?
Answer: Highest Common Factor.
Question 36. What is the GCD of the expressions xyz, 5x, and 3xp?
Answer: x.
Question 37. What is the GCD of 5 and 3?
Answer: 1.
Question 38. Determine the GCD of 8x^2 y^2 z and 10x^3 y^2 z^3.
Answer: 2x^2 y^2 z.
Question 39. What are the prime factors of the expression 3xp?
Answer: 3, x, and p.
Question 40. What is the GCD of 3x^3 y^2 and 2x^2 y^3?
Answer: x^2 y^2.
Question 41. What is the GCD of 3xy, 6x^2 y, and 9xy^2?
Answer: 3xy.
Question 42. List the prime factors of the expression 10x^3 y^2 z.
Answer: 2, 5, x, x, x, y, y, z, and z.
Question 43. List the prime factors of the expression 6xy.
Answer: 2, 3, x, and y.
Question 44. List the prime factors of the expression (x^2 - 25).
Answer: (x + 5) and (x - 5).
Question 45. List the prime factors of the expression (x - 5)^2.
Answer: (x - 5) and (x - 5).
Question 46. List the prime factors of the expression 3x + 9.
Answer: 3 and (x + 3).
Question 47. Write the formula for finding the volume of a box.
Answer: Volume of a box = Length × Width × Height.
Question 48. What is the common multiple of the expressions xyz and xyp?
Answer: xyzp.
Question 49. What is the common multiple of the expressions xy and x^2 y^2?
Answer: x^2 y.
Question 50. What is the common multiple of the expressions xy, x^2 y, and xy^2?
Answer: x^2 y^2.
Question 51. What is the greatest common divisor of 3 and 12?
Answer: 3.
Question 52. What is the greatest common divisor of 6, 9, and 12?
Answer: 3.
Question 53. What is the LCM of xyz, 5x, and 3xp?
Answer: 15xyzp.
Question 54. What is the LCM of 3x^3 y^2 and 2x^2 y^3?
Answer: 6x^3 y^3.
Question 55. If the length, width, and height of a box are x meters, y meters, and z meters respectively, what is the volume of the box?
Answer: xyz cubic meters.
Question 56. What is the common factor of xyz and xyp?
Answer: xy.
Question 57. What is the LCM of 5x^2 y^2, 10xz^3, and 15y^3 z^4?
Answer: 30x^2 y^3 z^4.
Question 58. What is the GCD of 3a^2 b^2 c^2 and 6ab^2 c^2?
Answer: 3ab^2 c^2.
Question 59. List the prime factors of 24.
Answer: 2, 2, 2, 3.
Question 60. If the width of a rectangle is 14xy and the area is 42xy^3, what is its length?
Answer: 3y^2.
Question 61. What is the English term for গসাগু?
Answer: Highest Common Factor (HCF).
Question 62. What is the GCD of 1 and 2?
Answer: 1.
Question 63. What is the LCM of 1 and 2?
Answer: 2.
Question 64. What is the GCD of xy and xz?
Answer: x.
Question 65. What is the LCM of xy and xz?
Answer: xyz.
Question 66. What is the GCD of x, x^2, x^3, and x^4?
Answer: x.
Question 67. What is the LCM of x, x^2, x^3, and x^4?
Answer: x^4.
Question 68. What is the GCD of 3 and 6?
Answer: 3.
Question 69. What is the LCM of 6 and 9?
Answer: 18.
Question 70. What is the LCM of xy, x^2 y, and xy^2?
Answer: x^2 y^2.
Question 71. Write the LCM of 3xy^2 z^2 and 6x^2 y^2 z^4.
Answer: 6x^2 y^2 z^4.
Question 72. What is the full form of লসাগু?
Answer: লঘিষ্ঠ সাধারণ গুণিতক.
Question 73. What is the full form of LCM?
Answer: Lowest Common Multiple.
Question 74. What is লসাগু called in English?
Answer: Lowest Common Multiple or LCM.
Question 75. What is the LCM of 3x^2 y^3 and 9x^3 y^2?
Answer: 9x^3 y^3.
Question 76. What is the LCM of 5x^2 y^2, 10xz^3, and 15y^3 z^4?
Answer: 30x^2 y^3 z^4.
Question 77. What is the common multiple of xyz and xyp?
Answer: xyzp.
Question 78. What is each of x, y, z called in x, y, z, or xyz?
Answer: Multiplicand.
