Highest Common Factor (H.C.F.):
The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly.
Methods of finding the H.C.F. of a given set of numbers:
Factorization Method: Expression each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives H.C.F.
Division Method: Suppose we have to find the H.C.F. of two given numbers. Divide the larger number by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is the required H.C.F.
Finding the H.C.F. of more than two numbers:
Suppose we have to find the H.C.F. of three numbers then, H.C.F. of [(H.C.F. of any two) and (the third number)] gives the H.C.F. of three given numbers.
Least Common Multiple (L.C.M.):
The least number which is exactly divisible by each one of the given numbers is called their L.C.M.
Factorization Method of Finding L.C.M.: Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of highest powers of all the factors.
Common Division Method (Short-cut Method) of Finding L.C.M.: Arrange the given numbers in a row in any order Divide by a number which divides exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required L.C.M. of the given numbers.
H.C.F. and L.C.M. of Fractions:
H.C.F. = HCF of numerators/LCM of denominators
L.C.M. = LCM of numerators/HCF of denominators
H.C.F. and L.C.M. of Decimal Fractions:
In given numbers, make the same number of decimal places by annexing zeros in some numbers, if necessary. Considering these numbers without decimal point, find H.C.F. or L.C.M. as the case may be. Now, in the result, mark off as many decimal places as are there in each of the given numbers.