64 is the smallest. It has these 7 factors: 1,2,4,8,16,32, and 64.
Which number has the smallest number of divisors?
In fact 120 is the smallest number having 16 divisors.
What is a distinct divisor?
Abstract. A set of positive integers is said to have the distinct divisor property if there is an injective map that sends every integer in the set to one of its proper divisors.
What is the number of positive divisors?
The divisors (or factors) of a positive integer are the integers that evenly divide it. For example, the divisors of 28 are 1, 2, 4, 7, 14 and 28. Of course 28 is also divisible by the negative of each of these, but by “divisors” we usually mean the positive divisors.
What is the smallest number to have over 300 divisors?
9 has 3 divisors: 1, 3, and 9. 11 is prime, so it has 2 divisors. 12 has 6 divisors: 1, 2, 3, 4, 6, and 12.
Is 0 A divisor of any number?
1 and -1 divide (are divisors of) every integer, every integer is a divisor of itself, and every integer is a divisor of 0, except by convention 0 itself (see also Division by zero). Numbers divisible by 2 are called even, and numbers not divisible by 2 are called odd.
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).
Which is the smallest positive integer with exactly 20 divisors?
So the answer is 3 unique primes (6 primes altogether). This is the maximum number of prime numbers that can divide this composite number with 20 factors. c) So the smallest positive integer that has exactly 20 positive divisors will be
What is the smallest number of primes that could divide an integer?
(a) A certain positive integer has exactly 20 positive divisors. What is the smallest number of primes that could divide the integer? (b) A certain positive integer has exactly 20 positive divisors.
Which is the smallest number with H divisors?
Given h = q 1 q 2 … q n, with primes q 1 ≤ q 2 ≤ ⋯ ≤ q n, let A ( h) be the smallest number with h divisors. The primary objective of the paper is to determine the exceptions. We call these numbers ordinary, from R. Brown, The minimal number with a given number of divisors, Journal of Number Theory 116 (2006) 150-158.
How many divisors are in the number 2 ^ 19?
The number 2^19 has twenty divisors, all of the form 2^n where n is an integer going from 0 to 19. The only prime involved is the number 2. . A) is 1, just like Alan said.
