**Hint:** Arrange the numbers in a row in order to determine the factors of a given number.

**Question.1.** Jagat arranges 21 marbles into rows such that each row has equal number of marbles. If there are 3 rows each having (a)_ marbles indicating that (b)_ and (c)_ are the factors of 21. Which of these options correctly identifies a, b and c?

(a) a = 3, b = 3, c = 7

(b) a = 18, b = 3, c = 7

(c) a = 7, b = 3, c = 7

(d) a = 10, b = 7, c = 3

**Question.2.** In a sitting arrangement, some people are made to sit in 9 rows such that each row has 4 people. If the same number of people are rearranged in m rows with n number of people in each row, which of these cannot be the value of m and n?

(a) 12 and 3

(b) 8 and 5

(c) 18 and 2

(d) 6 and 6

**Ans.1.** (c) a = 7, b = 3, c = 7**Ans.2.** (b) 8 and 5

**Hint:** Determine the numbers which exactly divide the given number in order to find the factors.

**Question.3.** Which of these is a factor of 96?

(a) 43

(b) 14

(c) 16

(d) 36

**Question.4.** The factors of a number 667 are consecutive prime numbers 𝑝 and 𝑞, 𝑝 > 𝑞. What is/are the factor(s) of the number (𝑝 − 𝑞)?

(a) 2 and 3

(b) 2 and 13

(c) 7

(d) 52

**Ans.3.** (c) 16**Ans.4.** (a) 2 and 3

**Hint:** Write the factors of a given number in order to determine prime and composite numbers.

**Question.5.** Which of these can be concluded about the number 713?

(a) As it has no factor other than 1 and itself, it is a prime number.

(b) As it has two factors 23 and 31 other than 1 and itself, it is a prime number.

(c) As it has two factors 23 and 31 other than 1 and itself, it is a composite number.

(d) As it has no factor other than 1 and itself, it is a composite number.

**Question.6.** What are the factors of 1147? Is it a prime number or a composite number?

(a) 1, 1147; composite

(b) 1, 1147; prime

(c) 1, 31, 37, 1147; composite

(d) 1, 31, 37, 1147; prime

**Ans.5.** (c) As it has two factors 23 and 31 other than 1 and itself, it is a composite number.**Ans.6.** (c) 1, 31, 37, 1147; composite

**Hint:** Apply the rules of divisibility in order to find the factors of a number quickly.

**Question.7.** A number 57a2b is divisible by 9 and 36b2 is divisible by 11, where a and b are the missing digits. Which of these could be the relation between a and b?

(a) a = 2b

(b) b – a = 3

(c) ab

(d) a – b = 3

**Question.8.** A 4-digit number 51𝑚2 is divisible by 3, where 𝑚is the missing digit. Which of these cannot be the value(s) of 𝑚?

(a) 1, 5, 9

(b) 1

(c) 4

(d) 1, 4, 7

**Ans.7.** (d) a – b = 3**Ans.8.** (a) 1, 5, 9

**Hint:** Factorise a number through prime factorisation in order list the primes factors.

**Question.9.** The prime factorisation of 145 is _.

(a) 5 × 29

(b) 3 × 3 × 3 × 531

(c) 1× 145

(d) 1× 4 × 5

**Question.10.** The information below describes three numbers, X, Y and Z.**X:** Greatest 2-digit number whose prime factorisation consists of only the factors 2 and 3.**Y:** A number whose prime factorisation consists of only the factors 2, 3 and 11.**Z:** It is a whole number having value equal to Y ÷ X.

Based on the given description of the numbers, a student makes two conclusions.**Conclusion I:** The prime factorisation of Y could be 2 × 2 × 3 × 3 × 11.**Conclusion II:** X = 96.

Which conclusion is correct?

(a) only conclusion I

(b) only conclusion II

(c) both the conclusions

(d) neither of the conclusions

**Ans.9.** (a) 5 × 29**Ans.10.** (b) only conclusion II

**Hint:** List down the common factors of given numbers in order to determine their HCF.

**Question.11.** If p is the greatest number which divides both 144 and 96, which of these is the greatest common factor of p – 3 and p + 2?

(a) 48

(b) 5

(c) 450

(d) 2880

**Question.12.** Which option lists the common factors of 212 and 112 and determines the greatest number that divides both of them?

(a) 212 × 112

(b) 2

(c) 2 × 2

(d) 4 × 28 × 53

**Ans.11.** (b) 5**Ans.12.** (c) 2 × 2

**Hint:** List down the common multiples of given numbers in order to determine their LCM.

**Question.13.** Which is smallest number divisible by both 48 and 76?

(a) 912

(b) 4

(c) 28

(d) 264

**Ans.13.** (a) 912

**Hint:** List down the common multiples of given numbers in order to determine their LCM.

**Question.14.** Consider the conditions about the numbers m and n:**Condition 1:** both are 2-digits numbers**Condition 2:** one is odd and one is even

If m × n = 180, what is the smallest common multiple of m and n?

(a) 60

(b) 90

(c) 180

(d) 36

**Ans.14.** (a) 60

**Hint:** Evaluate the factors of given two or more numbers in order to find the common factors and multiples.

**Question.15.** p exactly divides the numbers 42 and 70. Which of these could be a possible prime number that divides p?

(a) 14

(b) 3

(c) 7

(d) 5

**Question.16.** The numbers which exactly divide 75 and 45 are ___________.

(a) 3, 5 and 15

(b) 15 and 25

(c) 3, 15 and 25

(d) 9 and 15

**Ans.15.** (c) 7**Ans.16.** (a) 3, 5 and 15

**Hint:** Apply the concept of HCF in order to solve related real-life problems.

**Question.17.** Rajan has 36 candies of type A, 45 candies of type B and 18 candies of type C. He wants to pack candies in boxes such that:

- same type candies are packed in each box with no candies leftover
- each box has the same number of candies

What would be least number of boxes required by Rajan for packing?

(a) 11

(b) 180

(c) 99

(d) 9

**Question.18.** Nisha has 28 inches long red ribbon and 36 inches long green ribbon. For a craft project, she needs both colored ribbon pieces of equal lengths. What is the greatest length she can have for each piece assuming that all ribbon is used?

(a) 4 inches

(b) 64 inches

(c) 8 inches

(d) 252 inches

**Ans.17.** (a) 11**Ans.18.** (a) 4 inches

**Hint:** Apply the concept of LCM in order to solve related real-life problems.

**Question.19.** Three friends Deepak, Suman and Ravi are members of a library. Deepak visits the library every third day; Suman visits every fifth day and Ravi visits on every Sunday. If they met on 12th April, Sunday, after how many days they will meet again?

(a) 7

(b) 105

(c) 280

(d) 15

**Question.20.** Jagat has a jar of different coloured marbles. He is using them to make packs of marbles such that each pack has 12 red, 15 blue and 9 green marbles. After making packs, there are no marbles left in the jar.

What is the least possible number of marbles that could be in the jar at the beginning?

(a) 12

(b) 180

(c) 360

(d) 3

**Ans.19.** (b) 105**Ans.20.** (b) 180