Given a number, the task is to check if a number is divisible by 4 or not. The input number may be large and it may not be possible to store even if we use long long int.
Input : n = 1124 Output : Yes Input : n = 1234567589333862 Output : No Input : n = 363588395960667043875487 Output : No
Since input number may be very large, we cannot use n % 4 to check if a number is divisible by 4 or not, especially in languages like C/C++. The idea is based on following fact.
A number is divisible by 4 if number formed by last two digits of it is divisible by 4.
For example, let us consider 76952 Number formed by last two digits = 52 Since 52 is divisible by 4, answer is YES.
How does this work?
Let us consider 76952, we can write it as 76942 = 7*10000 + 6*1000 + 9*100 + 5*10 + 2 The proof is based on below observation: Remainder of 10i divided by 4 is 0 if i greater than or equal to two. Note than 100, 1000, ... etc lead to remainder 0 when divided by 4. So remainder of "7*10000 + 6*1000 + 9*100 + 5*10 + 2" divided by 4 is equivalent to remainder of following : 0 + 0 + 0 + 5*10 + 2 = 52 Therefore we can say that the whole number is divisible by 4 if 52 is divisible by 4.
Below is implementation of above fact :
This article is contributed by DANISH_RAZA . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Check if a large number is divisible by 11 or not
- Check if a larger number divisible by 36
- Difference of two large numbers
- Check if a large number is divisible by 9 or not
- Check if a large number is divisible by 8 or not
- Number of Permutations such that no Three Terms forms Increasing Subsequence
- Check if the first and last digit of the smallest number forms a prime
- Print all substring of a number without any conversion
- Complement of a number with any base b
- Check if Decimal representation of an Octal number is divisible by 7