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How many prime numbers lie between 1 and 30?
10
8
9
11
10
Remember the mnemonic: 4-4-2-2-3-2-2-3-2-1 for primes in each decade. For 1-30, we count the first three groups: 4 (up to 10) + 4 (11-20) + 2 (21-30) = 10.
Prime numbers between 1 and 30.
P={2,3,5,7,11,13,17,19,23,29}
Remember the mnemonic: 4-4-2-2-3-2-2-3-2-1 for primes in each decade. For 1-30, we count the first three groups: 4 (up to 10) + 4 (11-20) + 2 (21-30) = 10.
Including 1 as a prime number. Remember, 1 is neither prime nor composite; it only has one factor.
Define Prime Numbers
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
n>1,divisors={1,n}
Identify Primes from 1 to 10
The primes are 2, 3, 5, and 7. (1 is excluded)
P1−10={2,3,5,7}→4 numbers
Identify Primes from 11 to 20
The primes are 11, 13, 17, and 19.
P11−20={11,13,17,19}→4 numbers
Identify Primes from 21 to 30
The primes are 23 and 29.
P21−30={23,29}→2 numbers
Total Count
Adding the counts from each interval: 4 + 4 + 2 = 10.
4+4+2=10
A is correct because there are exactly 10 prime numbers between 1 and 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Knowing the count of primes up to 100 (which is 25) helps significantly in solving probability and divisibility-based problems in competitive exams.
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