How do you calculate the number of divisors?

The formula for calculating the total number of divisor of a number ′n′ where n can be represent as powers of prime numbers is shown as. If N=paqbrc . Then total number of divisors =(a+1)(b+1)(c+1).

What is Big O of sqrt N?

6 Answers. Square root time complexity means that the algorithm requires O(N^(1/2)) evaluations where the size of input is N. As an example for an algorithm which takes O(sqrt(n)) time, Grover’s algorithm is one which takes that much time.

Are divisors and factors the same?

Divisor and factors The divisor is any number that divides another number. A factor, however, is a divisor that divides the number entirely and leaves no remainder. So, all factors of a number are its divisors. But not all divisors will be factors.

How do you find the factors of an efficient number?

Best Approach: If you go through number theory, you will find an efficient way to find the number of factors. If we take a number, say in this case 30, then the prime factors of 30 will be 2, 3, 5 with count of each of these being 1 time, so total number of factors of 30 will be (1+1)*(1+1)*(1+1) = 8.

Can you really count divisors?

To find the number of divisors you must first express the number in its prime factors. Example: How many divisors are there of the number 12? 12 = 2^2 x 3 The number 2 can be chosen 0 times, 1 time, 2 times = 3 ways. The number 3 can be chosen 0 times, 1 time = 2 ways.

How many positive divisors does 2 N?

2^n, and these are all factors of 2^n. Hence 2^n has n+1 divisors.

Is sqrt n faster than N?

8 Answers. They are not equivalent: sqrt(N) will increase a lot more quickly than log2(N).

Does square root or log grow faster?

Growth rates of functions Any root function grows faster than any power of the natural log function.

How many divisors does 432 have?

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