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How many distinct longest fACTOR strings are there for any given number?
one
What is factors that appear in a complete list of factors for a given number only once?
distinct factors
What is called when factors that appear in a complete list of factors for given number only once?
distinct factors
How many longest strings of factors are there for a given number?
For composite numbers, only one string of factors is the longest; the prime factorization.
Which of these numbers when given in their prime factorization form has the least number of distinct prime factors 80 100 144 289 441?
289 does.
How is the number of factors of a given number related to the number of rectangler arrays?
The number of factors of a given number corresponds to the different ways that number can be expressed as a product of two integers, which represents the possible dimensions of rectangular arrays. For instance, if a number has six factors, it can be arranged into rectangular arrays of dimensions that multiply to that number, such as 1x6, 2x3, and 3x2. Each unique pair of factors gives a distinct arrangement, illustrating the relationship between factors and rectangular arrays. Thus, the total number of factors directly determines the number of unique rectangular configurations possible for that number.
One of two factors of a given number?
If the given number has two factors, one of them is 1.
Do perfect squares have an even or odd set of prime factors?
FactorsPerfect squares have an odd number of factors. If you think of factor pairs, the pair of factor that when multiplied together equals the given number, you realize that there are two factors for each pair until you come to the factor that when squared equals the number. For example, the factor pairs of 16 are 1 x 16, 2 x 8, and 4 x 4, giving us the factors of 1, 2, 4, 8, and 16 - an odd number of factors.Prime FactorsHowever, the situation is different with prime factors. It will depend on whether you list every prime factor or only the distinct prime factors. There will always be an even number of prime factors because when you square a number, you double the prime factors, which means you have an even number. That is not the case for distinct prime factors, because when you square a number, you are not adding any additional distinct factors. So, in some cases, there will be an even number of distinct prime factors and sometimes an odd number. Some examples follow.4 = 2 x 2. There are two prime factors, but one distinct prime factor.36 = 2 x 2 x 3 x 3. There are four prime factors and two distinct prime factors.900 = 2 x 2 x 3 x 3 x 5 x 5. There are six prime factors and three distinct prime factors.
How do you know a number if its factors are given?
There are two ways in which the factors can be given. You are given all the prime factors (and their multiplicity). In that case simply multiply them all together. Or You are given each factor. In this case, the biggest of these is the number.
Is the number of factors of a given number is limited?
Yes.
What are the factors of 3 and 20?
A factor = a number which can be divided into the given number with no remainder so no, 3 is not a factor of 20
How do you find the cardinal number to a set?
Count the number of distinct elements in the set.
