Let (x) be defined for all positive integer values of x as the product of all even factors of 4x. For example, (3)=12x6x4x2=576. What is the value of (5)?
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f(5)=20*10*4*2=1600? check it.
To find the value of (5), we need to determine the product of all even factors of 4x, where x = 5.
First, let's find the even factors of 4x. The even factors of 4x are obtained by multiplying the even divisors of 4 by x. Since 4 only has one even divisor, which is 2, we have:
Even factors of 4x = 2 * x
Substituting x = 5:
Even factors of 4x = 2 * 5 = 10
So, the even factors of 4x when x = 5 are {10}.
Now, we need to find the product of these even factors.
Product of even factors of 4x = Product of {10} = 10
Therefore, the value of (5) is 10.
To find the value of (5), we need to calculate the product of all even factors of 4x, where x = 5.
Step 1: Find all the factors of 4x
For x = 5, the value of 4x is 20. The factors of 20 are 1, 2, 4, 5, 10, and 20.
Step 2: Identify the even factors
From the factors of 20, the even factors are 2 and 4.
Step 3: Calculate the product of the even factors
To find the value of (5), we multiply the even factors 2 and 4 together:
(5) = 2 * 4 = 8.
Therefore, the value of (5) is 8.