Samacheer Kalvi Class 5 Maths Solutions Term 2 Chapter 2 Numbers Exercise 2.2

Question 1. Choose the best answer:
(i) The number divisible by 5 with no remainder
(a) 14
(b) 535
(c) 447
(d) 316
Answer: (b) 535
In simple words: To check if a number is divisible by 5 without a remainder, its last digit must be either 0 or 5. Only 535 ends in 5 among the given options.

🎯 Exam Tip: Remember the divisibility rule for 5: a number is divisible by 5 if its unit digit is 0 or 5.

(ii) Pick the number which is not a multiple of 6.
(a) 18
(b) 26
(c) 72
(d) 36
Answer: (b) 26
In simple words: A multiple of 6 is a number you get when you multiply 6 by another whole number. 18 (6x3), 72 (6x12), and 36 (6x6) are all multiples of 6, but 26 is not.

🎯 Exam Tip: To find if a number is a multiple of 6, check if it is divisible by both 2 and 3. 26 is divisible by 2 but not by 3 (2+6=8, which is not a multiple of 3).

(iii) The common multiple of 4 and 8 among the given number is.
(a) 32
(b) 84
(c) 68
(d) 76
Answer: (a) 32
In simple words: A common multiple means the number can be divided evenly by both 4 and 8. 32 can be divided by 4 (4 x 8) and by 8 (8 x 4), making it a common multiple.

🎯 Exam Tip: When one number is a multiple of the other (like 8 is a multiple of 4), their common multiples are just the multiples of the larger number.

(iv) Factors of 6
(a) 1, 2, 3
(b) 1, 6
(c) 1, 2, 3, 6
(d) 2, 3
Answer: (c) 1, 2, 3, 6
In simple words: Factors are numbers that divide another number exactly, without leaving a remainder. For the number 6, its factors are 1, 2, 3, and 6 because 6 can be divided evenly by all these numbers.

🎯 Exam Tip: Always remember that 1 and the number itself are always factors of any whole number.

(v) Multiple of 9 is
(a) 79
(b) 87
(c) 29
(d) 72
Answer: (d) 72
In simple words: A multiple of 9 is any number you get when you multiply 9 by a whole number. Since \( 9 \times 8 = 72 \), 72 is a multiple of 9.

🎯 Exam Tip: To check if a number is a multiple of 9, add up its digits. If the sum is a multiple of 9, then the number itself is a multiple of 9 (e.g., for 72, 7+2=9, which is a multiple of 9).

Question 2. Fill in the blanks:

Question 1. Factors of 7 ______
Answer: 1, 7
In simple words: The numbers that divide 7 exactly are 1 and 7. Since 7 is a prime number, it only has two factors: 1 and itself.

🎯 Exam Tip: Prime numbers always have exactly two factors: 1 and the number itself.

Question 2. The only even prime number is ______
Answer: 2
In simple words: The number 2 is special because it's the only even number that is also a prime number. All other even numbers can be divided by 2, so they have more than two factors.

🎯 Exam Tip: Remember that an even number is any number divisible by 2, and a prime number has only two factors: 1 and itself.

Question 3. L.C.M of 4, 12 ______
Answer: 12
In simple words: The Least Common Multiple (LCM) is the smallest number that is a multiple of both 4 and 12. Since 12 is a multiple of 4 (\( 4 \times 3 = 12 \)), 12 is the smallest common multiple.

🎯 Exam Tip: If one number is a multiple of another, their LCM is always the larger number.

Question 4. L.C.M of 5, 15 ______
Answer: 15
In simple words: The smallest number that both 5 and 15 can divide into evenly is 15. This is because 15 is a multiple of 5 (\( 5 \times 3 = 15 \)).

🎯 Exam Tip: You can find the LCM by listing multiples of each number until you find the first common one.

Question 5. The numbers which divides 35 without reminders are ______
Answer: 1, 5, 7
In simple words: The numbers that divide 35 completely, without any remainder, are called its factors. These are 1, 5, and 7. For example, \( 35 \div 5 = 7 \) and \( 35 \div 7 = 5 \).

🎯 Exam Tip: To find factors, you can start from 1 and go upwards, checking for exact divisions.

Question 3. Write down the factors of the given numbers.
(i) 25
(ii) 36
(iii) 14
(iv) 16
(v) 12
Answer:
(i) Factors of 25 are 1, 5, 25.
(ii) Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
(iii) Factors of 14 are 1, 2, 7, 14.
(iv) Factors of 16 are 1, 2, 4, 8, 16.
(v) Factors of 12 are 1, 2, 3, 4, 6, 12.
In simple words: To find the factors of a number, list all the whole numbers that can divide it exactly, leaving no remainder. Every number always has 1 and itself as factors.

🎯 Exam Tip: When listing factors, it's helpful to list them in pairs (e.g., for 12: 1x12, 2x6, 3x4) to ensure you don't miss any.

Question 4. Draw a picture of factor tree.
(i) 18
(ii) 33
(iii) 16
(iv) 50
Answer:
(i) Factor tree for 18:
       18
     /   \
    2     9
         /   \
        3    3
(ii) Factor tree for 33:
       33
     /   \
    3    11
(iii) Factor tree for 16:
       16
     /   \
    2     8
         /   \
       2    4
            /   \
           2    2
(iv) Factor tree for 50:
       50
     /   \
    2    25
         /   \
       5    5
In simple words: A factor tree helps break down a number into its prime factors. You keep dividing the number by prime numbers until all the end branches are prime numbers themselves.

🎯 Exam Tip: Always make sure the numbers at the very bottom of each branch (the leaves of the tree) are prime numbers.

Question 5. Write down the first 5 multiples of the given numbers.
(i) 7
(ii) 9
(iii) 16
(iv) 11
(v) 21
Answer:
(i) First 5 multiples of 7 are 7, 14, 21, 28, 35.
(ii) First 5 multiples of 9 are 9, 18, 27, 36, 45.
(iii) First 5 multiples of 16 are 16, 32, 48, 64, 80.
(iv) First 5 multiples of 11 are 11, 22, 33, 44, 55.
(v) First 5 multiples of 21 are 21, 42, 63, 84, 105.
In simple words: Multiples of a number are what you get when you multiply that number by other whole numbers (like 1, 2, 3, and so on). The first five multiples mean multiplying by 1, 2, 3, 4, and 5.

🎯 Exam Tip: The first multiple of any number is always the number itself.

Question 6. Find first three common multiples of the given numbers.
(i) 24, 16
(ii) 12, 9
(iii) 24, 36
Answer:
(i) For 24 and 16:
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, ...
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, ...
First three common multiples of 24 and 16 are 48, 96, 144.
(ii) For 12 and 9:
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, ...
First three common multiples of 12 and 9 are 36, 72, 108.
(iii) For 24 and 36:
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, ...
Multiples of 36 = 36, 72, 108, 144, 180, 216, ...
First three common multiples of 24 and 36 are 72, 144, 216.
In simple words: To find common multiples, list out the multiples for each number until you find the numbers that appear in both lists. The common multiples are the numbers shared by both lists.

🎯 Exam Tip: It is usually easier to start listing multiples from the larger number in the pair to find common multiples more quickly.

Question 7. Find L.C.M of the given numbers.
(i) 12 and 28
(ii) 16 and 24
(iii) 8 and 14
(iv) 30 and 20
Answer:
(i) For 12 and 28:
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, ...
Multiples of 28 = 28, 56, 84, 112, 140, 168, 196, ...
Common multiples of 12 and 28 are 84, 168, ...
The Least Common Multiple (LCM) is 84.
(ii) For 16 and 24:
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, ...
Multiples of 24 = 24, 48, 72, 96, 120, 144, ...
Common multiples of 16 and 24 are 48, 96, 144, ...
The Least Common Multiple (LCM) is 48.
(iii) For 8 and 14:
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, ...
Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, ...
Common multiples of 8 and 14 are 56, 112, ...
The Least Common Multiple (LCM) is 56.
(iv) For 30 and 20:
Multiples of 30 = 30, 60, 90, 120, 150, 180, 210, 240, 270, ...
Multiples of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, ...
Common multiples of 30 and 20 are 60, 120, 180
The Least Common Multiple (LCM) is 60.
In simple words: The LCM is the smallest positive number that is a multiple of two or more given numbers. You can find it by listing the multiples of each number until you find the first one they share.

🎯 Exam Tip: For smaller numbers, listing multiples works well. For larger numbers, prime factorization can be a faster method to find the LCM.

Question 8. Ramya visits the gym five days once and Kavitha visits the gym six days once. In which day will they meet each other?
Answer:
Multiples of 5 (Ramya's visits) = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, ...
Multiples of 6 (Kavitha's visits) = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, ...
The common multiples of 5 and 6 are 30, 60.
The Least Common Multiple (LCM) of 5 and 6 is 30.
So, Ramya and Kavitha will meet each other on the 30th day.
In simple words: To find when they meet again, we need to find the smallest day number that is a multiple of both 5 and 6. This is called the Least Common Multiple, which is 30.

🎯 Exam Tip: Word problems involving "when will they meet again" or "when will they happen simultaneously" usually require finding the Least Common Multiple (LCM).

Question 9. Arun and Shahjahan goes for walking in a circular path of a park in the same direction. Arun takes 6 minutes to complete one round, while Shahjahan takes 8 minutes to completed one round. In how many minutes will they meet each other?
Answer:
Multiples of 6 (Arun's round times) = 6, 12, 18, 24, 30, 36, 42, 48, 54, ...
Multiples of 8 (Shahjahan's round times) = 8, 16, 24, 32, 40, 48, 56, 64, ...
The common multiples of 6 and 8 are 24, 48, ...
The Least Common Multiple (LCM) of 6 and 8 is 24.
They will meet each other after 24 minutes.
In simple words: We need to find the earliest time (in minutes) when both Arun and Shahjahan will be at the starting point together again. This is found by calculating the Least Common Multiple (LCM) of 6 and 8, which is 24.

🎯 Exam Tip: When two people or objects move on a circular path and you need to find when they will meet again at the starting point, always use LCM.