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