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.
