The product of divisors of 7056 is –Select an answerA(84)48B(84)44C(84)45DNone of these
Question
The product of divisors of 7056 is –Select an answer
A(84)48
B(84)44
C(84)45
DNone of these
Solution
The product of the divisors of any number n is equal to n^(d/2), where d is the number of divisors of n.
First, let's find the prime factorization of 7056.
7056 = 2^4 * 3^2 * 7^2
The total number of divisors d is given by multiplying the exponents of the prime factors, each increased by one.
d = (4+1) * (2+1) * (2+1) = 5 * 3 * 3 = 45
So, the product of the divisors of 7056 is 7056^(45/2) = (84)^45
So, the correct answer is C(84)45.
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