The product of divisors of 512
Answers
Factors are 1,2,4,8,16,32,64,128,256,512!!!
Questions :- find The product of divisors of 512 ?
Concept used :-
Fundamental theorem of arithmetic states that every composite number can be expressed as a product of two or more prime numbers.
Let N be a composite number and a,b & c are its prime factors. Then :
N = a^p * b^q * c^r
Than, we Have :-
- Number of factors = (p+1)(q+1)(r+1)
- Number of unique factors = 3
- Number of prime factors = p+q+r
- Sum of factors = (a^0+a^1+..+a^p)(b^0+b^1+..+b^q)(c^0+c^1+..+c^r)
- Product of factors = N^(Number of factors/2)
Solution :-
Prime factors of 512 are :-
→ 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2⁹
So,
→ N = a^p
→ 512 = 2⁹
Therefore,
→ Number of factors of 512 = (p + 1) = (9 + 1) = 10.
Hence,
→ Product of factors = N^(Number of factors/2)
→ Product of factors = 512^(10/2)
→ Product of factors = (512)⁵. (Ans.)
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