Check if a large number is divisible by 4 or not
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.
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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 idea :
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