A is a factor of 720. A itself has exactly three
factors. How many values of A are possible?
Answers
Step-by-step explanation:
Given :-
A is a factor of 720. A itself has exactly three factors.
To find :-
How many values of A are possible?
Solution :-
Given number = 720
It can be written as
720 = 1×720
720 = 2×360
720 = 3×240
720 = 4×180
720 = 5×144
720 = 6×120
720 = 8×90
720 = 9×80
720 = 10×72
720 = 12×60
720 = 15×48
720 = 16×45
720 = 18×40
720 = 20×36
720 = 24×30
720 = 30×24
720 = 36×24
720 = 40×18
720 = 45×16
720 = 48×15
720 = 60×12
720 = 72×10
720 = 80×9
720 = 90×8
720 = 120×6
720 = 144×5
720 = 180×4
720 = 240×3
720 = 360×2
720 = 720×1
Factor of 720 = 1,2,3,4,5,6,8,9,10,12,
15,16,18,24,30,36,40,45,48,60,72,80,
90,120,180,240,360,720.
Given that
The factor of 720 = A
Number of factors of A = 3
Factors of 4 = 1,2,4
Number of factors of 4 = 3
Factors of 9 = 1,3,9
Number of factors of 9 = 3
So Among all factors of 720 , 4 and 9 has exactly 3 factors each.
So , The possible values of A = 4 and 9
The number of values of A = 2
Answer:-
The number of possible values of A is 2