Factors are numbers that can be divided into other numbers to get the same number in smaller parts. For example, when we divide a number, say, 12, into any other number, say, 6, we are getting the same number in smaller parts. This is called factorization of the given number. Factorsare nothing but divisors of the given number. For example, if you divide 12 by 6, the resulting number is two. This means that 12 is divisible by 6. The number is called a factor of 12 (since 12 is divisible by 6). Factors of a number are numbers that divide the number evenly.
As a factor is nothing but the number that we divide the given number into evenly, factors are always smaller. Factors of a number are always positive. Since the number is divisible by the factor when divided by the factor, factors always have a direct relationship with the number. Factors of a number are always less than the number. Thus, below are some of the properties of factors.
- The number of factors of a number is finite. This means that there is a maximum number of factors of a number. For example, the number of factors of 12 is 6 since 6 is the maximum number of factors of 12. The number of factors of any number is equal to the product of the prime factorization of that number and the number of its digits.
- A factor of a number cannot be greater than the number itself or it is always less than or equal to the number itself. For example factors of 12 are 1, 2, 3, 4, 6, and 12. This proves that the factors of a number are never greater than the number itself.
- If a number has two factors, then it is said to be a prime factor of that number. A number is prime when it has only one factor. Moreover, every number has atleast two factors i.e 1 and the number itself except 0 and 1. For example, the number 8 has factors 1, 2, 4, and 8. Thus, 8 has atleast two factors 1 and the number itself with other factors 2 and 4.
- Division and multiplication are the two most used operations in mathematical equations. The division is used to find the factors of a given number. The division is done by dividing the number to be divided by the given number. Similarly, multiplication is also used to find the factors of a given number.
Two methods can be used to find the factors of a given number. The two methods are Division and Multiplication.
- Division– Division is used to find the factors of a given number. The division is done by dividing the number to be divided by the given number. For example, if we want to find the factors of 12, we divide 12 by 6 to get factors. We can say that division is the process of finding the factors of a number using the method of dividing the number to be divided by the given number.
- Multiplication-The second method used to find the factors of a given number is Multiplication. Multiplication is used to find the factors of a given number. Multiplication is done by multiplying the factors of the number and by finding different combinations. For example, if we want to find the factors of 12, we multiply 2 by 6, 4 by 3, 12 by 1. Thus, it can be seen that the factors of 12 are 1, 2, 3, 4, 6, and 12.
The study of factors is very important for anyone who wants to become a good mathematician. It helps you in understanding the basic building blocks of numbers and helps you in solving mathematical equations.
If you are interested in learning more about the subject and concepts like factors, prime factorization, and greatest common factor then you should read from Cuemath. They have systematic and comprehensive material on the subject of factors.
