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How many prime numbers are there between 1 and 50?
13
14
15
16
16
Memorize the count of primes in intervals: 1-10(4), 11-20(4), 21-30(2), 31-40(3), 41-50(2). Sum: 4+4+2+3+2 = 15.
Range of numbers is between 1 and 50.
n=count of prime numbers in [1,50]
Memorize the count of primes in intervals: 1-10(4), 11-20(4), 21-30(2), 31-40(3), 41-50(2). Sum: 4+4+2+3+2 = 15.
Students often include 1 as a prime number, but 1 is neither prime nor composite. Additionally, miscounting 49 (which is 72) or 51 (which is 3×17) is common.
Define Prime Numbers
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
P={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47}
List Primes from 1 to 50
Identify all prime numbers strictly between 1 and 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
Primes=15
Verification
Counting the listed primes: 1(2), 2(3), 3(5), 4(7), 5(11), 6(13), 7(17), 8(19), 9(23), 10(29), 11(31), 12(37), 13(41), 14(43), 15(47). The total count is 15.
Total Count=15
D is correct because there are exactly 15 prime numbers between 1 and 50, which are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.
Knowing the distribution of primes up to 100 is helpful for divisibility tests and solving LCM/HCF problems efficiently in competitive exams.
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