Prime Numbers Between 1 and 100: 17 MCQs with answers

C · A whole number greater than 1 with exactly two factors: 1 and itself.

A prime number has exactly two distinct factors: 1 and itself. Having more than two factors makes a number composite, and not all odd numbers are prime (e.g., 9, 15).

B · 9

9 = 3 × 3, so it has three factors (1, 3, 9) and is composite. 2, 3, and 7 each have exactly two factors.

D · 25

There are exactly 25 primes between 1 and 100, from 2 up to 97. This is written as π(100) = 25.

B · No, because it has only one factor, not exactly two.

1 has only one factor (itself), so it does not meet the definition of a prime number, which requires exactly two distinct factors. 1 is neither prime nor composite.

A · True

There are exactly 25 prime numbers between 1 and 100.

C · 15

15 is odd but composite (15 = 3 × 5), so it has more than two factors. 11, 13, and 17 are all prime, so they do not disprove the statement.

B · 2, 3, 5, and 7

Since √100 = 10, you only need to test primes up to 10, which are 2, 3, 5, and 7. If none divide the number evenly, it is prime.

C · The number is definitely prime.

If a number under 100 has no prime factor among 2, 3, 5, and 7, then it has no prime factor ≤ √100 = 10, so it must be prime.

B · 91

91 = 7 × 13, so it is composite. 97, 89, and 83 are all prime (none is divisible by 2, 3, 5, or 7).

C · (3, 5)

Twin primes differ by 2. (3, 5) differ by 2 and are both prime. (2, 3) differ by 1, (7, 11) by 4, and (13, 17) by 4.

B · $2^2 \times 3 \times 7$

84 = 4 × 21 = 2² × 3 × 7. The other options either contain composite factors (14, 4, 21) or give the wrong product (2³ × 3 × 7 = 168).

B · 9 should not be in the list because 9 = 3 × 3.

9 is composite (9 = 3 × 3), so it should not appear in a list of primes. The correct primes under 20 are 2, 3, 5, 7, 11, 13, 17, 19.

A · You cross out multiples of each prime starting from 2, and the remaining numbers are prime.

The sieve works by crossing out multiples of each prime (2, 3, 5, 7) in turn; the numbers left uncrossed are prime. Crossing out only multiples of 2 and 3 would leave composites like 25 and 49.

C · 97

97 is prime (not divisible by 2, 3, 5, or 7). 87 = 3 × 29, 91 = 7 × 13, and 99 = 9 × 11 are all composite.

A · 53

53 is prime. 51 = 3 × 17, 57 = 3 × 19, and 55 = 5 × 11 are all composite.

D · There are more primes between 1 and 50 than between 50 and 100.

There are 15 primes between 1 and 50, but only 10 between 50 and 100. Primes become less frequent as numbers increase, though 97 is prime between 90 and 100.

B · 97

The last prime number circled when using the Sieve of Eratosthenes up to 100 is 97, as it is the largest prime number in that range. All numbers greater than 97 are either composite or exceed 100.