# How do you find the smallest number with certain numbers divisors?

## How do you find the smallest number with certain numbers divisors?

and the divisors of 16 are 2k where k = 0, 1, 2, 3, or 4. This approach generalizes: For any prime q, the smallest number with q divisors is 2q-1.

## What is the smallest positive integer that has exactly k divisors?

64 is the smallest. It has these 7 factors: 1,2,4,8,16,32, and 64.

How do you find the smallest divisor?

Approach:

1. Check if the number is divisible by 2 or not.
2. Iterate from i = 3 to sqrt(N) and making a jump of 2.
3. If any of the numbers divide N then it is the smallest prime divisor.
4. If none of them divide, then N is the answer.
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### What is the smallest number with 12 divisors?

So 60 is the smallest number with 12 divisors.

### What is the smallest number to have over 300 divisors?

Hence the smallest positive integer with eight divisors is 24.

How do you find the number of divisors in a number?

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 the smallest positive integer having 8 positive divisors?

smallest positive integer that has exactly eight distinct…

• 1 Answers. #1. The smallest positive integer is: 42 = (1, 2, 3, 6, 7, 14, 21, 42) > 8 (divisors) Guest Nov 16, 2020.
• 27 Online Users.

#### What is the smallest positive integer with exactly 20 positive divisors?

240
240 is the smallest integer with exactly 20 positive divisors.

How do you find the smallest factor?

The quickest way to find the factors of a number is to divide it by the smallest prime number (bigger than 1) that goes into it evenly with no remainder. Continue this process with each number you get, until you reach 1.

## How do you find the smallest divisors of a number in Python?

Python Program to Find the Smallest Divisor of an Integer

1. Take in an integer from the user.
2. Use a for loop where the value of i ranges from 2 to the integer.
3. If the number is divisible by i, the value of i is appended to the list.
4. The list is then sorted and the smallest element is printed.
5. Exit.
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## What is the smallest number with exactly 14 divisors?

Find the smallest number having 14 factors. We have 14 = 7 x 2, and subtracting unity from each we obtain 6 and 1 as exponents to apply to any primes we wish. To derive the smallest number, we must obviously apply our exponents to the smallest primes, namely 2 and 3 which results in N = 2^6 x 3^1 = 192.

What is the smallest number with 15 divisors?

What are the smallest positive integers with 15 divisors? – Quora. Since 15=3*5 the positive integers with 15 divisors are either in the form p^4*q^2 or in the form p^14, where p and q are prime numbers. The sixth would be 2025.

### How do you find the k-th value of a vector?

Simple Approach: A simple approach is to run a loop from 1 to √N and find all factors of N and push them into a vector. Finally, sort the vector and print the K-th value from the vector. Note: Elements in the vector will not be sorted initially as we are pushing both factors (i) and (n/i).

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### How do you find the number of divisors of a given number?

The first answer in MrocKK’s link is useful, although hard to understand. A better source may be here: you can calculate the number of divisors directly from the prime factorization of the number. Since you’re looking for exactlya power of 2 divisors, this tells you that every prime factor in your answer must occur one less than a power of 2.

What is the smallest number with 32 divisors?

Give your answer modulo 500500507. It’s simple enough to count the divisors of n, eg. in Python len([i for i in range(1,n+1) if n \% i == 0]). This is O(n). I tried brute force search and found the smallest number with 32 divisors is 840, but it’s much too slow for the problem above.

#### What is the minimum value of n for fixed D(N)?

For fixed d(n)(as in your case), the minimum value of nis obviously obtained by carefully selecting powers of existing primes, or by adding new primes. Let’s work through this simple example, 16: d(x) = (a1+1)(a2+1)… (ak+1) = 16 = 24. This means that you have at most 4 different primes, therefore: x = 2a1* 3a2*5a3* 7a4 where ai>= 0.