LCM AND HCF

LCM AND HCF
Division Method
We find the H.C.F two given numbers using the steps given below 
Step  I : Divide the larger number by the smaller number.
Step II : Divide the divisor by the remainder
Step III: Repeat the process of dividing the preceding divisor by the remainder last obtained, till remainder '0'  is obtained. 
    Then, the last divisor is the required H.C.
Example I : Find the H.C.F of 1965 and 2096.
Solution : Using division method, we have
    Hence, the H.C.F of 1965 and 2096 is 131
Note : H.C.F of three numebers
H.C.F of 3 numbers = H.C.F of (any two and 3rd number)

Co-primes :
    Two numbers are said to be co-primes if their H.C.F is '1
Example: HCF of 161 and 192 by division method         
Sol :Let us find the H.C.F of 161 and 192  by division method.
    We have, H.C.F of 161 and 192 is '1'
    Hence 161 and 192 are co-primes

Note :  
        1) H.C.F of two distinct prime numbers is one
        2) H.C.F of two co-primes is one
        3) H.C.F of an even number and an odd number is one
        4) H.C.F of two consecutive even numbers is '2'.
        5) If a and b are co-primes then write (a,b) =1 
            [H.C.F of a and b is 1]
        some examples :
        (15, 16) =1, ( 20, 22) =2