Suppose we have to calculate the HCF of two higher numbers, finding factors will be difficult, so we go for alternative method, division method. For example suppose we have to find the HCF of the numbers 2520 and 1225, let us first find the factors of the two numbers.

\(2520{\rm{ }} = {\rm{ }}{2^3} \times {3^2} \times {5^1} \times {7^1}\) and \(1225{\rm{ }} = {\rm{ }}{5^2} \times {7^2}\)

Clearly HCF of the two numbers will be \(5 \times 7{\rm{ }} = {\rm{ }}35\).

Some times finding factors is not that easy, in these type of cases we must the following division method. Let’s take the following example.

Example 10: Find the HCF of 4003 and 1003

Solution: 

Last divisor which gives 0 remainder, is the required HCF. Hence HCF in this example is 1.