Math, asked by bharathbt1910, 8 months ago

The product of divisors of 512

Answers

Answered by theaditisingh12
4

Factors are 1,2,4,8,16,32,64,128,256,512!!!

Answered by RvChaudharY50
1

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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