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How many prime numbers less than 100 are there that when divided by 5 leaves an odd remainder?

+2 votes
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How many prime numbers less than 100 are there that when divided by 5 leaves an odd remainder?
posted Apr 10, 2017 by Nikita Sehgal

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2 Answers

+2 votes

The only possible odd remainders from dividing number by 5 seem to be 1 and 3. The remainder of dividing by 5 in 10-based notation depends only on the last digit since every non zeroth power of 10 is divisable by 5.
From all digits from 0 to 9 only 1, 3, 6 and 8 would give the remainder of 1 or 3.
Since primes beside 2 must all be odd numbers, then all primes ending with 1 and 3 seem to be the only primes which when divided by 5 leave an odd remainder.
Hence for primes less than 100 they would be

3, 11, 13, 23, 31, 41, 43, 53, 61, 71, 73, 83

answer May 21, 2017 by anonymous
0 votes

2,3,11,13,23,31,41,43,53,61,71,73,83are only prime no. Which leave odd reminder when divided by 5.

answer Apr 10, 2017 by Pratyush Pathak



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