Number of Factors of an Integer

Introduction to number of factors of an integer:

In math, the natural numbers are form the integer and another name of an integer is whole number. The factor is divisor of a given number. This divisor is divides the given integer without any remainder. The factors may be two or more in an integer. Now we are going to see about number of factors of an integer.

Explanation for Number of Factors of an Integer

Some notes about integer and factors in math:

An integer may be positive and negative. We can’t calculate the number of factors of decimal or fraction.

The integer has one or more divisors. We can classify the factors into two. The names of factors are prime and composite. The prime factor is defining the prime number that is prime number has only two factors. The composite factor is defining the composite number that is the composite number has more than two factors.

We can count the number of factors of integer by listing method. We can separate the normal factors and prime factors.

More about Number of Factors of an Integer

Example problems for number of an integer in math:

Problem 1: Count how much number of factors and prime factors are present in given integer.

94

Answer:

Given integer are 94.

The given integer 94 has 4 factors as 1, 2, 47, 94 and 2 prime factors are present as 2 x 47.

Problem 2: Count how many number of factors present in given integer?

112

Answer:

Given integer are 112.

The given integer has 10 factors. They are 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112.

It has 5 prime factors. They are 2 x 2 x 2 x 2 x 7.

Exercise problems for number of factors of an integer:

1. How many numbers of factors in integer 75?

Answer: The integer 75 has 6 factors as 1, 3, 5, 15, 25, and 75.

2. How many numbers of factors in integer 19?

Answer: The integer 19 has 2 factors.

The Various Types of Sets in Set Theory

One of the important theories in modern mathematics is the set theory. This theory has been present now for a very long time. This was developed during the 1870’s itself. There are various operations in the set theory. Set is basically a collection of objects. When it comes to sets in mathematics, the objects must be related to mathematics. There is the presence of a universal set in set theory. This acts as the reference set. Other sets are compared with the same. Set theory is best explained with the help of Venn diagrams. The operation on sets like union, intersection, and compliment and so on can be well represented with the help of Venn diagrams. The subset R contains some of the elements present in R and not all the elements.’ R’ acts as the universal set in this case. The concepts sets and subsets are closely related. Without the presence of one the other doesn’t exist. The definition of subset is that it is a set which contains some of the elements present in the original set.

An example can be used to explain the concept. A set has elements {x, y, z} and another one contains {x). The latter set is the subset of the former one. There can be a number of subsets of the same set. If there was another set containing the element {y}, then it also becomes the subset of the given set.  The subset notation is used to convey that a particular set is the subset of the other set. The other set is called the super set. It contains all the elements present in the subset and the subset contains some of the elements of the super set. This is nothing but the subset is a part of the super set.

Set theory can be very helpful in solving mathematical problems. The Venn diagrams give a clear picture on the sets and their operations. By the Venn diagrams problems can be solved. So, lot of arithmetical calculations can be avoided. The process also becomes very simple and easy to understand. Once one is thorough with the concepts of the set theory, the problems can be very easily solved. One of the important operations in set theory is that of intersection of two sets. The intersection of two sets yields a new set which contains the common elements of both the sets.