In mathematics, any number that helps to perform the arithmetic operation of division can be defined as the factors. This term has been excavated or derived from the words of Latin which signifies ‘a doer’ or ‘performer’. In order to find the factors of any value, two arithmetic operations can be used: either multiplication or division. The uses of it.
can be seen in our everyday life as well, let us take some examples so that you get a basic overview of it. Example 1: When your teacher asks you to divide the rows and columns into equal parts, find the answer to some calculations. Example 2: When you go traveling or exchange money. In all the above examples, the use of factors is very prominent. In this article, we will try to cover some related topics such as the properties of factors and do a detailed analysis.
Properties of Factors
As mentioned above, any number that helps to perform the arithmetic operation of division can be defined as the factors. Like every other term of mathematics, factors also possess some properties which are very significant. The following points analyses the significant properties of factors.
- When you calculate the factors of a given number, the resultant value or factors are always smaller or equal to the value of the number given. For example, factors of 5 are 1 and 5, here no factor is greater than 5.
- Every other number in mathematics has two factors except the number 1 and 0. The number 1 consists of only one factor that is the number itself.
- The process of division and multiplication can be used to find the factors of a given number.
- The total numbers of a factor will always be finite.
Greatest/Highest Common Factors
There can be more than two factors of a given number (exception = 1 and 0), the factor which is the greatest or highest can be regarded as the greatest common factor or greatest common divisor. In short, the highest common factor is also known as the HCF or the GCF. Generally, there are three methods given to find the factors of two or more numbers. They are – the division method, the prime factorization method, and the listing out of the common factors method. In the next few sections, we may try to solve some calculations about finding the greatest common factors between two numbers.
Some Calculations based on the Greatest Common Factors
Till now, you may have understood the factors and their types. Let us solve some questions about it so that you get conceptual clarity about the topic. The following are a few examples.
Example 1: Find the highest common factor of the numbers 10 and 15?
Numbers given = 10 and 15
Now, find out the factors of 10 and 15,
Factors of 10 = 2* 5
Factors of 15 = 3 * 5
The factors of 10 and 15 are = 2 * 3 * 5 * 5.
Amongst them, the highest common factor of 10 and 15 is 5.
Therefore, the greatest common divisor of 15 and 10 is equivalent to 5.
Example 2: Find the highest common factor of the numbers 18 and 27?
Numbers given = 18 and 27
Now, find out the factors of 18 and 27,
Factors of 18 = 18, 9, 6, 3, 2 and 1
Factors of 27 = 27, 9, 3 and 1
The common factors of 18 and 27are = 3, 9 and 1
Amongst them, the highest common factor of 18 and 27 is 9.
Therefore, the greatest common divisor of 18 and 27 is equivalent to 9.
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