Question:- How many factors does 3600 have?
A. 45
B. 44
C. 43
D. 42
Answer:-
Factor of 3600 = 2 X 2 X 3 X 3 X 2 X 2 X 5 X 5 = (2)4 X (3)2 X (5)2
No. of total Factors = (2)4+1 X (3)2+1 X (5)2+1 = 5 X 3 X 3 = 45
No. of total Even Factors = (2~even)4 X (3~odd)2+1 X (5~odd)2+1 = 4 X 3 X 3 = 36
No. of total Odd Factors = (2~even)4 X (3~odd)2+1 X (5~odd)2+1 = 3 X 3 = 9
No. of total Prime Factors = (2)4 X (3)2 X (5)2 = 4 + 2 + 2 = 8
3600 have total factors = (2)4+1 X (3)2+1 X (5)2+1 = 5 X 3 X 3 = 45
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