Numbers of ways in which 75600 can be resolved as product of two divisors which are relatively prime ?
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Solution :-
First we will have to find the prime factors of 75600.
Prime Factorization of 75600 = 2*2*2*2*3*3*3*5*5*7
75600 = 2⁴ × 3³ × 5² × 7
The number of ways in which a composite number N can be resolved as product of two divisors which are relatively prime to each other
= 2^(n - 1), where N is the number of different factors of N
⇒ 2^(n - 1)
⇒ 2^(4 - 1)
⇒ 2^3
= 8 ways
Answer.
First we will have to find the prime factors of 75600.
Prime Factorization of 75600 = 2*2*2*2*3*3*3*5*5*7
75600 = 2⁴ × 3³ × 5² × 7
The number of ways in which a composite number N can be resolved as product of two divisors which are relatively prime to each other
= 2^(n - 1), where N is the number of different factors of N
⇒ 2^(n - 1)
⇒ 2^(4 - 1)
⇒ 2^3
= 8 ways
Answer.
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