GSEB Class 6 Maths Solutions Chapter 3 Playing With Numbers Exercise 3.1

Gujarat Board Textbook Solutions Class 6 Maths Chapter 3 Playing With Numbers Ex 3.1

 

Question 1. Write all the factors of the following numbers:
(a) 24
(b) 15
(c) 21
(d) 27
(e) 12
(f) 20
(g) 18
(h) 23
(i) 36
Answer:
(a) 24
As, \( 24 = 1 \times 24 \)
\( 24 = 2 \times 12 \)
\( 24 = 3 \times 8 \)
\( 24 = 4 \times 6 \)
The factors of 24 include: 1, 2, 3, 4, 6, 8, 12, and 24.
(b) 15
As, \( 15 = 1 \times 15 \)
\( 15 = 3 \times 5 \)
The factors for 15 are: 1, 3, 5, and 15.
(c) 21
As, \( 21 = 1 \times 21 \)
\( 21 = 3 \times 7 \)
The factors of 21 are: 1, 3, 7, and 21.
(d) 27
As, \( 27 = 1 \times 27 \)
\( 27 = 3 \times 9 \)
The factors of 27 include: 1, 3, 9, and 27.
(e) 12
As, \( 12 = 1 \times 12 \)
\( 12 = 2 \times 6 \)
\( 12 = 3 \times 4 \)
The factors for 12 are: 1, 2, 3, 4, 6, and 12.
(f) 20
As, \( 20 = 1 \times 20 \)
\( 20 = 2 \times 10 \)
\( 20 = 4 \times 5 \)
The factors of 20 include: 1, 2, 4, 5, 10, and 20.
(g) 18
As, \( 18 = 1 \times 18 \)
\( 18 = 2 \times 9 \)
\( 18 = 3 \times 6 \)
The factors of 18 are: 1, 2, 3, 6, 9, and 18.
(h) 23
As, \( 23 = 1 \times 23 \)
The factors of 23 are: 1 and 23.
(i) 36
As, \( 36 = 1 \times 36 \)
\( 36 = 2 \times 18 \)
\( 36 = 3 \times 12 \)
\( 36 = 4 \times 9 \)
\( 36 = 6 \times 6 \)
The factors for 36 include: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
In simple words: To find all the factors of a number, list all the pairs of numbers that multiply together to give that number. Make sure to include 1 and the number itself.

Exam Tip: Remember that factors always come in pairs. If a number is prime, its only factors will be 1 and itself.

 

Question 2. Write first five multiples of:
(a) 5
(b) 8
(c) 9
Answer:
(a) 5
As, \( 5 \times 1 = 5 \)
\( 5 \times 2 = 10 \)
\( 5 \times 3 = 15 \)
\( 5 \times 4 = 20 \)
\( 5 \times 5 = 25 \)
The first five multiples of 5 are: 5, 10, 15, 20, and 25.
(b) 8
As, \( 8 \times 1 = 8 \)
\( 8 \times 2 = 16 \)
\( 8 \times 3 = 24 \)
\( 8 \times 4 = 32 \)
\( 8 \times 5 = 40 \)
The initial five multiples of 8 are: 8, 16, 24, 32, and 40.
(c) 9
As, \( 9 \times 1 = 9 \)
\( 9 \times 2 = 18 \)
\( 9 \times 3 = 27 \)
\( 9 \times 4 = 36 \)
\( 9 \times 5 = 45 \)
The first five multiples of 9 are: 9, 18, 27, 36, and 45.
In simple words: To find the multiples of a number, multiply that number by 1, then by 2, then by 3, and so on. Each result is a multiple.

Exam Tip: The first multiple of any number is always the number itself. Multiples go on forever, but questions usually ask for a specific number of them.

 

Question 3. Match the items in column 1 with the items in column 2.

Answer:
(i) \( \rightarrow \) (b) (Since \( 7 \times 5 = 35 \))
(ii) \( \rightarrow \) (d) (Since \( 15 \times 2 = 30 \))
(iii) \( \rightarrow \) (a) (Since \( 8 \times 2 = 16 \))
(iv) \( \rightarrow \) (f) (Since \( 20 \times 1 = 20 \))
(v) \( \rightarrow \) (e) (Since \( 25 \times 2 = 50 \))
In simple words: We pair each number from Column 1 with the description in Column 2 that correctly relates to it, either as a multiple or a factor. For example, 35 is a multiple of 7 because 7 times 5 equals 35.

Exam Tip: For matching questions, test each option by checking if it's a factor (divides evenly) or a multiple (can be formed by multiplying). If one match works, proceed to the next to save time.

 

Question 4. Find all the multiples of 9 upto 100.
Answer:
As, \( 9 \times 1 = 9 \)
\( 9 \times 2 = 18 \)
\( 9 \times 3 = 27 \)
\( 9 \times 4 = 36 \)
\( 9 \times 5 = 45 \)
\( 9 \times 6 = 54 \)
\( 9 \times 7 = 63 \)
\( 9 \times 8 = 72 \)
\( 9 \times 9 = 81 \)
\( 9 \times 10 = 90 \)
\( 9 \times 11 = 99 \)
All the multiples of 9 up to 100 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99.
In simple words: To find multiples of 9 up to 100, just keep multiplying 9 by whole numbers (1, 2, 3, etc.) until the answer goes over 100. List all the results that are 100 or less.

Exam Tip: To ensure you don't miss any multiples or go over the limit, systematically multiply the given number by consecutive integers (1, 2, 3, ...), stopping once the product exceeds the specified upper bound.