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HCF Of two Number
March 6, 2024
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Python program to find HCF of Two Numbers
Definition & Explanation
The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder. To find the HCF of two numbers, various methods can be used, such as prime factorization, the Euclidean Algorithm, or brute-force checking of common factors. The HCF is crucial in simplifying fractions, finding equivalent fractions, and solving certain mathematical problems.
Example: Consider finding the HCF of the numbers 36 and 60.
Explanation of the Euclidean Algorithm:
- Start with the two numbers: 36 and 60.
- Divide the larger number (60) by the smaller number (36): 60 ÷ 36 = 1 remainder 24.
- Replace the larger number (60) with the smaller number (36) and the smaller number (36) with the remainder (24): new numbers are 36 and 24.
- Repeat the division: 36 ÷ 24 = 1 remainder 12.
- Again, replace the larger number (36) with the smaller number (24) and the smaller number (24) with the remainder (12): new numbers are 24 and 12.
- Repeat the division: 24 ÷ 12 = 2 remainder 0.
- The remainder becomes 0, indicating that 12 is the HCF of 36 and 60.
Therefore, the HCF of 36 and 60 is 12.
This method efficiently finds the HCF by repeatedly dividing the larger number by the smaller number and replacing the numbers until the remainder becomes zero, giving the HCF.
More Description
Program to find the HCF of Number
- Initialize
num1with the value 36 andnum2with the value 60. - Initialize
hcfwith the value 1. - Start a loop from
iequals 1 up to the minimum ofnum1andnum2, which is 36. - Check if both
num1andnum2are divisible by the current value ofi. - If
iis a divisor of bothnum1andnum2, updatehcfto the value ofi. - Repeat steps 4-5 until
ireaches the minimum ofnum1andnum2. - After the loop,
hcfwill contain the highest common factor ofnum1andnum2, which is 12 in this case. - Print the value of
hcf, which is 12.
This approach checks all numbers from 1 up to the minimum of num1 and num2 to find their highest common factor. While it’s simple, it may not be efficient for large numbers compared to other methods like prime factorization or the Euclidean Algorithm.
C
Method 1 :
#include <stdio.h>
int main() {
int num1 = 36;
int num2 = 60;
int hcf = 1;
for (int i = 1; i <= (num1 < num2 ? num1 : num2); i++) {
if (num1 % i == 0 && num2 % i == 0) {
hcf = i;
}
}
printf("HCF OF Number %d and %d is %d\n", num1, num2, hcf);
return 0;
}
Output :
HCF OF Number 36 and 60 is 12C++HCF OF Number 36 and 60 is 12
Method 1 :
#include <iostream>
using namespace std;
int main() {
int num1 = 36;
int num2 = 60;
int hcf = 1;
for (int i = 1; i <= min(num1, num2); i++) {
if (num1 % i == 0 && num2 % i == 0) {
hcf = i;
}
}
cout << "HCF OF Number " << num1 << " and " << num2 << " is " << hcf << endl;
return 0;
}
Output :
HCF OF Number 36 and 60 is 12JAVA
Method 1 :
public class Main {
public static void main(String[] args) {
int num1 = 36;
int num2 = 60;
int hcf = 1;
for (int i = 1; i <= Math.min(num1, num2); i++) {
if (num1 % i == 0 && num2 % i == 0) {
hcf = i;
}
}
System.out.println("HCF OF Number " + num1 + " and " + num2 + " is " + hcf);
}
}
Output :
HCF OF Number 36 and 60 is 12Python
Method 1 :
num1=36
num2=60
hcf=1
for i in range(1,min(num1,num2)):
if num1%i==0 and num2%i==0:
hcf=i
print("HCF OF Number",num1,"and",num2,"is",hcf)Output :
HCF OF Number 36 and 60 is 12DataTpoint, your ultimate destination for navigating the dynamic landscape of career opportunities in the data and technology realm.
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