GSEB Class 6 Maths Solutions Chapter 3 સંખ્યા સાથે Exercise 3.1

Gujarat Board Textbook Solutions Class 6 Maths Chapter 3 સંખ્યા સાથે Ex 3.1

Question 1. નીચેની સંખ્યાઓના તમામ અવયવો લખોઃ
(a) 24
(b) 15
(c) 21
(d) 27
(e) 12
(f) 20
(g) 18
(h) 23
(i) 36
Answer:
(a) 24
\( 24 = 1 \times 24 \), \( 24 = 2 \times 12 \), \( 24 = 3 \times 8 \), \( 24 = 4 \times 6 \).
Therefore, all factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
(b) 15
\( 15 = 1 \times 15 \), \( 15 = 3 \times 5 \).
Thus, all factors of 15 are 1, 3, 5, and 15.
(c) 21
\( 21 = 1 \times 21 \), \( 21 = 3 \times 7 \).
Hence, the complete set of factors for 21 includes 1, 3, 7, and 21.
(d) 27
\( 27 = 1 \times 27 \), \( 27 = 3 \times 9 \).
So, all the factors of 27 are 1, 3, 9, and 27.
(e) 12
\( 12 = 1 \times 12 \), \( 12 = 2 \times 6 \), \( 12 = 3 \times 4 \).
Consequently, all the factors for 12 are 1, 2, 3, 4, 6, and 12.
(f) 20
\( 20 = 1 \times 20 \), \( 20 = 2 \times 10 \), \( 20 = 4 \times 5 \).
Therefore, the entire set of factors for 20 consists of 1, 2, 4, 5, 10, and 20.
(g) 18
\( 18 = 1 \times 18 \), \( 18 = 2 \times 9 \), \( 18 = 3 \times 6 \).
Thus, the factors of 18 are 1, 2, 3, 6, 9, and 18.
(h) 23
\( 23 = 1 \times 23 \).
So, the only factors of 23 are 1 and 23. This means 23 is a prime number, as its factors are just 1 and itself.
(i) 36
\( 36 = 1 \times 36 \), \( 36 = 2 \times 18 \), \( 36 = 3 \times 12 \), \( 36 = 4 \times 9 \), \( 36 = 6 \times 6 \).
Consequently, all the factors for 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
In simple words: To find factors of a number, list all pairs of numbers that multiply to give that number. Each number in those pairs is a factor.

Exam Tip: Remember that 1 and the number itself are always factors. For prime numbers, these are the only two factors.

Question 2. પ્રથમ પાંચ અવયવી લખો:
(a) 5
(b) 8
(c) 9.
Answer:
(a) The first five multiples of 5 are:
\( 5 \times 1 = 5 \), \( 5 \times 2 = 10 \), \( 5 \times 3 = 15 \), \( 5 \times 4 = 20 \), \( 5 \times 5 = 25 \).
Thus, the first five multiples of 5 are 5, 10, 15, 20, and 25.
(b) The first five multiples of 8 are:
\( 8 \times 1 = 8 \), \( 8 \times 2 = 16 \), \( 8 \times 3 = 24 \), \( 8 \times 4 = 32 \), \( 8 \times 5 = 40 \).
Therefore, the initial five multiples of 8 include 8, 16, 24, 32, and 40.
(c) The first five multiples of 9 are:
\( 9 \times 1 = 9 \), \( 9 \times 2 = 18 \), \( 9 \times 3 = 27 \), \( 9 \times 4 = 36 \), \( 9 \times 5 = 45 \).
Thus, the first five multiples for 9 are 9, 18, 27, 36, and 45.
In simple words: To find multiples, multiply the given number by whole numbers like 1, 2, 3, and so on.

Exam Tip: Always remember that the first multiple of any number is the number itself (when multiplied by 1).

Question 3. ની સાથે ઊભી હરોળ 2ની સરખામણી કરોઃ
Answer:

Exam Tip: For matching questions, systematically check each option. A multiple is a product of two numbers, while a factor divides a number evenly.

Question 4. 100 સુધીના 9ના બધા અવયવી શોધો.
Answer: All multiples of 9 up to 100 are obtained as follows:
\( 9 \times 1 = 9 \), \( 9 \times 2 = 18 \), \( 9 \times 3 = 27 \), \( 9 \times 4 = 36 \), \( 9 \times 5 = 45 \), \( 9 \times 6 = 54 \), \( 9 \times 7 = 63 \), \( 9 \times 8 = 72 \), \( 9 \times 9 = 81 \), \( 9 \times 10 = 90 \), \( 9 \times 11 = 99 \).
Thus, all multiples of 9 up to 100 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99.
In simple words: To find all multiples of 9 up to 100, just keep adding 9 to the previous multiple until you go over 100.

Exam Tip: When asked for multiples up to a certain number, always make sure your last multiple does not exceed the given limit.