on external variable parameters (such as the time of dayand on the memory address of the object being hashed (because address of the object may change during processinguniformity good hash function must map the keys as evenly as possible over its output range this means that the probability of generating every hash value in the output range should roughly be the same the property of uniformity also minimizes the number of collisions different hash functions in this sectionwe will discuss the hash functions which use numeric keys howeverthere can be cases in real-world applications where we can have alphanumeric keys rather than simple numeric keys in such casesthe ascii value of the character can be used to transform it into its equivalent numeric key once this transformation is doneany of the hash functions given below can be applied to generate the hash value division method it is the most simple method of hashing an integer this method divides by and then uses the remainder obtained in this casethe hash function can be given as (xx mod the division method is quite good for just about any value of and since it requires only single division operationthe method works very fast howeverextra care should be taken to select suitable value for for examplesuppose is an even number then (xis even if is even and (xis odd if is odd if all possible keys are equi-probablethen this is not problem but if even keys are more likely than odd keysthen the division method will not spread the hashed values uniformly generallyit is best to choose to be prime number because making prime number increases the likelihood that the keys are mapped with uniformity in the output range of values should also be not too close to the exact powers of if we have (xx mod then the function will simply extract the lowest bits of the binary representation of the division method is extremely simple to implement the following code segment illustrates how to do thisint const / prime number int (int xreturn ( ) potential drawback of the division method is that while using this methodconsecutive keys map to consecutive hash values on one handthis is good as it ensures that consecutive keys do not collidebut on the otherit also means that consecutive array locations will be occupied this may lead to degradation in performance example calculate the hash values of keys and solution setting hash values can be calculated ash( ( multiplication method the steps involved in the multiplication method are as followsstep choose constant such that