The common factor of two numbers is very useful in mathematical calculations. This common factors are usually needed for simplifying the fractions. There are mainly two different methods that are used for finding the common factors between the numbers. The two approaches that can be undertaken for calculating the common factors. And there are two types of common factors: Highest Common Factors (HCF) and Lowest Common Factors (LCM).
Factors are those numbers that is used to multiple together to produce another number. For example, let us consider two numbers 2 and 3. 2 and 3 are the factors of 6 and 3 and 3 are the factors of 9. The prime numbers in the number system are the numbers that does not have any factors except the number itself and 1.
The prime numbers are known as the whole numbers that are obviously greater than 1 and the numbers that has one 1 as a factor and the number itself. Factors are the integers that are multiplied for getting other integers. The factors of a number is a whole number that can divide a particular number in to some another number. The first few of the prime numbers are 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 and 29. All the above stated numbers have exactly two factors and the numbers are not possible to be divided by other numbers. The factors of the prime numbers are 1 and the number itself. All other number in the number system except the prime numbers are known as composite numbers. The composite numbers are the numbers who has more than two factors are known as composite numbers. The number 1 in the number system is neither composite number nor prime number.
It can be stated that for all the prime numbers p, there is actually a prime number p’ and the p’ is greater than the number p. This statement includes a mathematical proof that was firstly demonstrated in the ancient times by a Greek mathematician Euclid. The mathematical proof helps to validate the concept that there is no availability of largest prime number. As the numbers in the number system increases, the total number of prime numbers in the number system becomes less frequent and prime number are found less frequently. It is difficult to find prime number with the increment of the natural numbers in number system. The largest known prime number that is available is the number that has more than 23 million digits and is generally written as M77232917. This number has one million more digits compared to the previously recorded number.
Since, in the above stated example 3 is the prime number and the two whole numbers that can be multiplied to get the number 3 is 3 itself and 1. To find out the common factors, it is always helpful to find out the common factors that are prime of that number. The prime number breaks the number in many fundamental building blocks that plays an important role towards finding common factors between two numbers. The prime common factors are invaluable for finding the square roots of the number.
The simple way to find out the common factor of two numbers is simply listing the factors that are include din each number and choose the highest factors that are common in both the number. For example- let us take two number 45 and 60. The easiest way to find the common factors are to find out the prime factors of the numbers individually. Since 45 is the number, the prime factors included in the number 45 is 1 and 45. The next step is to find out whether the number 2 is the factor of the number 45. 2 is not the factor of 45. 3 is a factor of 45 as because 3 * 15 is 45. Next 5 is the factors of 45 since 5 * 9 is 45. So the factors of 45 is 1, 3, 5, 9, 15, and 45.
Similarly, conducting the same process the factors of the number 60 is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. So, comparing the list of factors between the two numbers, we get 1 and 15 as the common factors among the two numbers and the greatest common factors that can be identified from the number is 15.
There is also a second method to find the greatest common factor between two numbers. This method is known as prime factorization which much easier as well as structured method of finding out common factors. Prime factorization includes breaking down the number until there is left with only prime numbers.
Let us solve 56 and 120 by prime factorization method
Factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
So, the factors that are associated with the number 56 are 1, 2, and 7.
Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120
The common factor that is calculated from 56 and 120 is 1, 2, 4, and 8. And the greatest common factor is 8.
The two common way of finding out the factors of the number are stated above. Factors are the integers that are multiplied for getting other integers. The factors of a number is a whole number that can divide a particular number in to some another number. As the numbers in the number system increases, the total number of prime numbers in the number system becomes less frequent and prime number are found less frequently. It is difficult to find prime number with the increment of the natural numbers in number system. Under this condition there are only one even prime number that satisfies the condition of even number as well as satisfies the condition of prime numbers. Two is the only number that can be stated as even prime number. Two is the number is has two visible factors. The number two is divided by the 1 and is also can be divided by the number itself.
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