Ncert solutions

Ncert solutions

Grade 6

Playing With Numbers | Exercise 3.1

Question 1

Q1) Write all the factors of the following numbers :

(i) 24

(ii) 15

(iii) 21

(iv) 27

(v) 12

(vi) 20

(vii) 18

(viii) 23

(ix) 36

SOLUTION:

(i). The factor of 24 are as follows:

24\ =\ 1\times\ 24\

24\ =\ 12\ \times2\

24\ =\ 3\times\ 8\

24\ =\ 4\ \times\ 6

24\ =\ 12\ \times\ 2

24\ =\ 6\times4

24=8\times3\

24=\ 24\times1

therefore, the factors of 24 are 24 = 1, 2, 3, 4, 6, 12 and 24.

(ii) The factor of 15 are as follows:

15=\ 1\times1\ 5

15\ =\ 3\times5\

15\ =\ 5\times\ 3

15=15\times1

therefore, the factors of 15 are 1, 3, 5 and 15.

(iii) The factors of 21 are as follows:

21\ =\ 1\times21\ \ \

21\ =\ 3\times7\

21\ =\ 7\times3\

21\ =\ 21\ \times1\

therefore, the factors of 21 are 1, 3, 7 and 21.

(iv) The factors of 27 are as follows:

27\ =\ 1\times27\

27\ =\ 3\times9\

27\ =\ 9\times3

27\ =\ 27\times1

therefore, the factors of 27 are 1, 3, 9 and 27.

(v) The factors of 12 are as follows:

12\ =\ 1\times12

12\ =\ 2\times6\

12\ =\ 3\ \times4\

12\ =\ 4\times3\

12\ =\ 4\ \times3\

12\ =\ 6\times2\

12=\ 12\times1

Therefore, the factors of 12 are 1, 2, 3, 4, 6 and 12.

(vi) the factors of 20 are as follows:

20\ =\ 1\times20

20\ =\ 2\times10

20\ =\ 4\times5

20=\ 10\times2

20\ =\ 5\times4

20=20\times1

therefore, the factors of 20 are 1, 2, 4, 5 10 and 20.

(vii) the factors of 18 are as follows:

18=1\times18\

18\ =\ 2\times9

18=\ 3\times6\

18=\ 6\times3\

18=\ 9\times2

18=18\times1

therefore, factors of 18 are 1,2, 3, 6, 9 and 18.

(viii) the factors of 23 are as follows:

23=1\times23

23=23\times1

therefore, the factors of 23 are 1 and 23.

(ix) the factors of 36 are as follows:

36=1\times36

36=2\times18\

36=\ 3\times12

36=4\times9

36=6\times6

36=\ 18\times2

36=12\times3

36=9\times4

36=\ 36\times1

therefore, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

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subject-cta

Question 1

Q1) Write all the factors of the following numbers :

(i) 24

(ii) 15

(iii) 21

(iv) 27

(v) 12

(vi) 20

(vii) 18

(viii) 23

(ix) 36

SOLUTION:

(i). The factor of 24 are as follows:

24\ =\ 1\times\ 24\

24\ =\ 12\ \times2\

24\ =\ 3\times\ 8\

24\ =\ 4\ \times\ 6

24\ =\ 12\ \times\ 2

24\ =\ 6\times4

24=8\times3\

24=\ 24\times1

therefore, the factors of 24 are 24 = 1, 2, 3, 4, 6, 12 and 24.

(ii) The factor of 15 are as follows:

15=\ 1\times1\ 5

15\ =\ 3\times5\

15\ =\ 5\times\ 3

15=15\times1

therefore, the factors of 15 are 1, 3, 5 and 15.

(iii) The factors of 21 are as follows:

21\ =\ 1\times21\ \ \

21\ =\ 3\times7\

21\ =\ 7\times3\

21\ =\ 21\ \times1\

therefore, the factors of 21 are 1, 3, 7 and 21.

(iv) The factors of 27 are as follows:

27\ =\ 1\times27\

27\ =\ 3\times9\

27\ =\ 9\times3

27\ =\ 27\times1

therefore, the factors of 27 are 1, 3, 9 and 27.

(v) The factors of 12 are as follows:

12\ =\ 1\times12

12\ =\ 2\times6\

12\ =\ 3\ \times4\

12\ =\ 4\times3\

12\ =\ 4\ \times3\

12\ =\ 6\times2\

12=\ 12\times1

Therefore, the factors of 12 are 1, 2, 3, 4, 6 and 12.

(vi) the factors of 20 are as follows:

20\ =\ 1\times20

20\ =\ 2\times10

20\ =\ 4\times5

20=\ 10\times2

20\ =\ 5\times4

20=20\times1

therefore, the factors of 20 are 1, 2, 4, 5 10 and 20.

(vii) the factors of 18 are as follows:

18=1\times18\

18\ =\ 2\times9

18=\ 3\times6\

18=\ 6\times3\

18=\ 9\times2

18=18\times1

therefore, factors of 18 are 1,2, 3, 6, 9 and 18.

(viii) the factors of 23 are as follows:

23=1\times23

23=23\times1

therefore, the factors of 23 are 1 and 23.

(ix) the factors of 36 are as follows:

36=1\times36

36=2\times18\

36=\ 3\times12

36=4\times9

36=6\times6

36=\ 18\times2

36=12\times3

36=9\times4

36=\ 36\times1

therefore, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

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