Calculation for HCF

HCF can be calculated using two methods. These are Prime Factorization Method and Division method. These two methods are discussed below:

HCF by Prime Factorisation Method

As the name suggests, in this method we first find the prime factors of the given numbers and using the prime factors of the given numbers we find the HCF. Let’s understand it with the help of an example.

Example: Find the HCF 16 and 72 using prime factorisation method.

Solution:

Step 1: find the prime factors of all the given numbers.

16 = 2 x 2 x 2 x 2

72 = 2 x 2 x 2 x 3 x 3

Step 2: Check the common factors between them.

Common factors between 16 and 72 = 2 x 2 x 2

Step 3: Multiply the common values to get the final answer

HCF ( 16, 72) = 2 x 2 x 2 = 8

HCF by Division Method

In this method we divide the larger number by the smaller number out of the two given number of which we have to find the HCF. We successively divide the previous divisior by the obtained remainder. This process continues till the remainder isn zero. Let’s understand it with an example.

Example: Find the HCF of 12 and 18 by Division Method.

Solution:

Step 1: Begin by writing down the numbers you want to find the HCF for. For this example, let’s use 12 and 18.

Step 2: Divide 18 by 12 i.e. 18 ÷ 12, Q₁ = 1, R₁ = 6

Step 3: Divide the previous divisor i.e. 12 by the remainder i.e. 6. This means now 12 is the dividend and 6 is the divisior. We get Q₂ = 2 and R₂ = 0

Step 4: Since, the Remainder is zero when the divisor is 6. Hence HCF is 6

Step 5: If the remainder would not have been zero then we would continue the process till we get the remainder to be zero. The divisor of the last step is the HCF of the numbers.

HCF (Highest Common Factor) and LCM (Least Common Multiple) are fundamental concepts in mathematics, particularly in number theory. HCF is the highest common number which can exactly divide the two given numbers. LCM or Lowest Common Multiple is the common number that is divisible by both the given numbers. These concepts are essential tools for solving a wide range of mathematical problems.

In this article, we will learn about the definitions of HCF and LCM, their properties, and methods for calculating HCF and LCM. Along with this, all the possible varieties of HCF and LCM Questions have been discussed with solutions, and practice questions are provided on HCF and LCM for learners.