Class 7 Math Chapter 9 Factor HCF And LCM

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)

√(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

(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

(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

(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

(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) $6x^3$

(d) $12x$

10. What are the factors of 9?

(a) 1, 3, 6

√(b) 1, 3, 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

√(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

(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) $2x^2 yz^2$

(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

(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

(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) $y$

(d) $xyz$

19. What is the GCD of $1, 3, 5$ ?

√(a) $1$

(b) $3$

(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

(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

√(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

(d) Remainder

24. What is the common multiple of $xyz$ and $xyp$ ?

(a) $xy$

(b) $p$

√(d) $xyzp$

25. What is the common factor of $xyz$ and $xyp$ ?

√(a) $xy$

(b) $xp$

(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

(d) Least Common Factor

28. What is the LCM of $2xy$ and $3xz$ ?

√(a) $6xyz$

(b) $xy$

(d) $yx$

29. What is the LCM of $6x^2 y$ and $12x^3 y^2$ ?

(a) $10x^3 y^2$

√(b) $12x^3 y^2$

(d) $9x^3 y^2$

30. What is the LCM of the expressions $xyz$ , $5x$ , and $3xp$ ?

(a) $xyz$

(b) $x$

√(d) $15xyzp$

31. What is the LCM of $3x^3 y^2$ and $2x^2 y^3$ ?

(a) $2x^2 y^2$

(b) $3x^2 y^2$

√(d) $6x^3 y^3$

32. What is the LCM of $5ab^2 x^2$ and $10a^2 b y^2$ ?

(a) $5ab$

√(b) $10a^2 b^2 x^2 y^2$

(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.

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Class 7 math chapter 9 factor HCF and LCM : MCQ and One word question