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Answer :
Final answer:
The question seeks the numbers from 1 to 3600 that are relative prime to 3600. To find this, we use the Euler Totient function, which provides us with the number of integers from 1 to 'n' that are relatively prime to 'n'. The correct answer is 2400, which is achieved after factoring 3600 into its prime factors and applying the Euler Totient function.
Explanation:
The question is asking us to find the number of integers from 1 to 3600 that are relative prime to 3600. 'Relative prime' means that the greatest common divisor (gcd) of the two numbers is 1. In other words, the numbers do not share any common factors aside from 1.
To find the numbers that are relative prime to 3600, we need to use a function called the Euler Totient function (often denoted by the Greek letter phi, φ). The Euler Totient function of a number 'n' represents the amount of integers from 1 to 'n' that is relatively prime to 'n'.
First, we need to factorize 3600 into its prime factors. 3600 = 2^5 * 3^2 * 5^2.
Then we apply the formula for the φ function which is: φ(n) = n*(1-1/p1)*(1-1/p2)*... Where the 'p' are the prime factors of 'n'. Substituting the prime factors we got before gives φ(3600) = 3600*(1-1/2)*(1-1/3)*(1-1/5) = 2400.
So, the correct answer is: D) 2400.
Learn more about Relative Primes here:
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