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The highest possible number that splits both numbers fully is called the Highest Common Factor (HCF). The largest common divisor is another name for the highest common factor (HCF) (GCD).
Finding the HCF of two numbers can be done in a variety of ways. The prime factorization method is one of the most efficient ways to calculate the HCF of two or more numbers. Examine the many characteristics and properties of HCF to learn more about it. Find out what the highest common factor is for a group of numbers, how to calculate it, how it relates to LCM, and other fascinating information.
HCF Definition
The greatest number among all the common factors of two or more numbers is the HCF (Highest Common Factor). The HCF (Highest Common Factor) of two natural integers x and y is the greatest number that divides both x and y. Let’s look at this definition with the help of two numbers: 18 and 27. 1, 3, and 9 are the common factors in 18 and 27. The greatest (biggest) number among these is 9. As a result, the HCF of 18 and 27 equals 9. HCF (18,27) = 9 is how it is written. To grasp this notion, look at the diagram below.
Difference between HCF and LCM
| LCM (Lowest Common Multiple) | HCF (Highest Common Factor) |
| The smallest number among all possible multiples of two or more numbers is the least frequent multiple. | The greatest number among all the common factors of two or more numbers is the highest common factor. |
| Their LCM factors are represented by the appropriate numbers. | Each of the numbers in an HCF of two or more is a factor. |
| The product is always the LCM of two or more prime numbers. | When two or more prime numbers are added together, the HCF always equals one. |
| When two or more integers are multiplied together, the LCM is always bigger than or equal to each of the numbers. | When two or more numbers are added together, the HCF is always less than or equal to each of them. |
The least common multiple (LCM) and the highest common factor (HCF) between two numbers are the least common multiple and the highest common factor, respectively.
The major goal of demonstrating the difference between these two numbers is to demonstrate the distinction between a factor and a multiple.
An integer that occurs in the timetable is a multiple of a whole number.
Consider the multiples of three, for example:
3, 6, 9, 12, 15, 18, and so on.
The factor of an integer, on the other hand, is the number that divides the integer without leaving any remainder.
Consider the 36 factors, for example:
1, 2, 3, 4, 6, 9, 12, 18, and 36.
To get the LCM and HCF of two different numbers, we must first find the highest common factor of 15 and 18, which is 3.
15 and 18 have an LCM of 90.
90 X 3 = 270 L.C.M x H.C.F
15 x 18 = 270 is the result of multiplying these two numbers.
As a result, the product of L.C.M and H.C.F is the same as the sum of these two quantities.
Properties of HCF
The highest common factor of numbers a and b is known as the HCF. Take a look at some of HCF’s key characteristics:
HCF has the following qualities.
HCF splits two or more numbers evenly, leaving no residue.
Each of the numbers in an HCF of two or more is a factor.
When two or more numbers are added together, the HCF is always less than or equal to each of them.
When two or more prime numbers are added together, the HCF always equals one.
Conclusion
The largest possible number that splits both integers exactly is the highest common factor (HCF).
HCF represents the HCF of a and b. (a, b).
If d is the HCF (a, b), the common factor of a and b cannot be bigger than d.
The largest common divisor is another name for the highest common factor (HCF) (GCD)
The product of the least powers of the common prime factors is the HCF of those numbers, which is one of the easiest ways to find it.
