Memory allocation is the process of assigning a portion of memory to a process for execution. Partitioning makes easier to organise memory requirement of different processes. It is accomplished through a procedure called memory management. Memory requirement of process may be either contiguous allocation or non -contiguous allocation. If process requirement is contiguous, then consecutive blocks of memory have to be allocated to the process. If the requirement is non -contiguous, then process may be allocated the blocks of memory scattered all around the memory space. The efficiency of memory management depends on the utilization of memory by the process. If the process is allotted exactly the amount of memory requested by it, then it results in the maximum utilization. On the other hand, if the process is allotted more memory than requested, then excess memory is wasted as it cannot be used by another process. Such wastage of memory is referred to as internal fragmentation that has to be minimized. If the process does not get its required contiguous memory due to total available free memory is in non -contiguous form, then, it is referred to as external fragmentation. This incident should also be avoided. All these aspects should be considered while computing the memory utilization. In this paper, we will discuss about some of the popular memory allocation algorithms that are, first fit, best fit and worst fit for fixed sized and variable sized partition of contiguous nature, their performance will be analysed along with internal and external fragmentation and the whole procedure of an algorithm will be illustrated with proper diagrams. The main objective of this paper is to determine the most efficient algorithm in contiguous memory allocation that as minimum fragmentation.