Question

(i) Is {1, 2, 4, 16, 64} = {x : x is a factor of 32} ? Give reason.

(ii) Is {x : x is a factor of 27} ≠ {3, 9, 27, 54} ? Give reason.

(iii) Write the set of even factors of 124.

(iv) Write the set of odd factors of 72.

Answer 1

(i) No, {1, 2, 4, 16, 64} ≠ {x : x is factor of 32} Because 64 is not a factor of 32

(ii) Yes, {x : x is a factor of 27} + {3, 9, 27, 54} Because 54 is not a factor of 27

(iii) 1 x 124 = 124 

2 x 62 = 124 

4 x 31 = 124 

Factors of 124 = 1, 2, 4, 31, 62, 124 

Set of even factors of 124 = {2, 4, 62, 124}

(iv) 1 x 72 = 72 

2 x 36 = 72 

3 x 24 = 72 

4 x 18 = 72 

6 x 12 = 72 

8 x 9 = 72 

Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 

Set of odd factors of 72 = {1, 3, 9}