HCF: Definition, Process, Methods, Examples

The highest number that divides each of the two or more numbers is the HCF or Highest Common Factor. The Greatest Common Factor (HCF) is also known as the Greatest Common Measure (GCM) or the Greatest Common Divisor (GCD). HCM and LCM are two alternative ways of finding the smallest common multiple of any two or more numbers. LCM, or Least Common Multiple, is used to discover the smallest common multiple of any two or more integers.

Key Terms: HCF, LCM, Greatest Common Factor, Greatest Common Divisor, Factors, Division, Number, Prime Number

Read More: Minors and Cofactors

---

Meaning of HCF

[Click Here for Sample Questions]

HCF stands for Highest Common Factor in its entire form. The highest factor that may evenly divide two numbers is the HCF of two numbers. HCF can be calculated using two or more numbers. It is the biggest divisor for any two or more numbers that can divide them evenly or fully.

For instance: Since 15 is the greatest number that can divide both 60 and 75 perfectly, it is the highest common factor of 60 and 75.

Read More: Natural Numbers and Whole Numbers

---

HCF Process

[Click Here for Sample Questions]

We can calculate the HCF of any pair of numbers using one of two methods:

• By prime factorization method

• By division method

Prime Factorization Method for HCF

To get the HCF of numbers using the prime factorisation method, follow the steps outlined below.

• Step 1: Each number should be written as a product of its prime components. Prime factorization is the name given to this procedure.
• Step 2: Make a list of the factors that both numbers have in common.
• Step 3: The HCF is the sum of all common prime factors ( use the lower power of each common factor)

Example 1: Examine the HCF values of 60 and 75.

Solution:

Example 2: Calculate the HCF for 36, 24 and 12.

Solution:

Example 3: Calculate the HCF for 36, 27, and 80.

Solution:

HCF Using Division Method

The division approach is just dividing the provided numbers at the same time to find the common factors between them. To solve HCF difficulties, follow the instructions outlined below.

• Step 1: Separate the given numbers with commas and write them horizontally in a sequence.
• Step 2: The smallest prime number that can divide the given integer is the smallest prime number. It should split the given numbers exactly. (Write on the left side of the page.)
• Step 3: Write the quotients now.
• Step 4: Repeat the procedure until there are no more co-prime numbers.
• Step 5: Because the factors on the left-hand side split all the integers exactly, we'll get the common prime factors. The HCF of the given numbers is the product of these common prime factors.

Read More: Real Numbers

Example 1: Consider the HCFs of 30 and 75.

As can be seen, the prime factors indicated on the left side split all the numbers perfectly. As a result, they're all prime factors in common. For the numbers at the bottom, there is no common prime factor.

Hence, HCF = 3 × 5 = 15.

Example 2: Determine the HCF of 36 and 24.

HCF = 2 × 2 × 3 = 12.

Example 3: Calculate the HCF of 36, 12, 24, and 48.

HCF = 2 × 2 × 3 = 12.

Read More: Prime Numbers

---

Shortcut approach for HCF

[Click Here for Sample Questions]

How to calculate the HCF of any pair of numbers.

• Step 1: First, divide the larger number by the smaller number, as in Larger Number/Smaller Number.
• Step 2: Step 1's divisor is divided by the remainder. Step 1/Remainder divisor
• Step 3: Step 2's divisor is divided by the residual once more.
• Step 2: Remainder divisor
• Step 4: Repeat the process until there is no longer any residual.
• Step 5: The HCF is the divisor of the final step.

---

Process To Calculate HCF Of Three Numbers

[Click Here for Sample Questions]

Here’s the processes for calculating HCF of three numbers that have been presented to us:

The procedures outlined above can also be used to calculate the HCF of more than three values.

---

HCF of Four Numerical Values

[Click Here for Sample Questions]

To get the HCF of four digits, use these simple steps:

• To begin, divide the four digits into two groups of two.
• Find the HCF of a two-number pair.
• Then, using the HCF of HCFs determined in the preceding step, get the HCF of HCFs.
• The final HCF will be the four-number HCF that is necessary.

---

HCF of Prime Numbers

[Click Here for Sample Questions]

Any two or prime numbers' HCF is always equal to one.

Since prime numbers are those that only have two factors: 1 or the number itself. As a result, if no other factor exists, the HCF of such numbers will be 1. The following are some examples:

• HCF (2, 3) = 1
• HCF (3, 7) = 1
• HCF (5, 13) = 1
• HCF (19, 23) = 1

Read More: Area of Rectangle

---

Things to Remember

• The highest number that divides each of the two or more numbers is the HCF or Highest Common Factor.
• When two or more numbers are divided by the HCF, each number is divided without a remainder.
• When two or more integers are added together, the HCF is always less than or equal to each of the numbers.
• When two or more prime numbers are added together, the HCF is always 1.
• Euclid devised a method for calculating the HCF.
• The HCF of two or more numbers divides the supplied numbers, the HCF of prime numbers is always equal to one. 
• The HCF of two or more numbers is always less than or equal to the given numbers.

Read More: Area of Square Using Diagonal