Euclid’s division lemma, states that for any two positive integers ‘a’ and ‘b’ we can find two whole numbers ‘q’ and ‘r’ such that

Euclid’s division lemma can be used to:
Find the highest common factor of any two positive integers and to show the common properties of numbers.
Finding H.C.F  using Euclid’s division lemma:
Suppose, we have two positive integers ‘a’ and ‘b’ such that ‘a’ is greater than ‘b’. Apply Euclid’s division lemma to the given integers ‘a’ and ‘b’ to find two whole numbers ‘q’ and ‘r’ such that, ‘a’ is equal to ‘b’ multiplied by ‘q’ plus ‘r’.

Check the value of ‘r’. If ‘r’ is equal to zero then ‘b’ is the HCF of the given numbers. If ‘r’ is not equal to zero, apply Euclid’s division lemma to the new divisor ‘b’ and remainder ‘r’. Continue this process till the remainder ‘r’ becomes zero. The value of the divisor ‘b’ in that case is the HCF of the two given numbers.
Euclid’s division algorithm can also be used to find some common properties of numbers.