Prime Numbers Quiz: Prime Numbers Practice From Basics to Divisibility Rules

36 = 2 times 18 = 2 times 2 times 9 = 2 times 2 times 3 times 3. Every factor in option B is prime. Option A includes 6, which is composite. Option C includes 4 and 9, both composite. Option D includes 12, which is composite. Only option B expresses 36 as a product of prime factors only.

Both 17 and 19 are prime — each is divisible only by 1 and itself. Option B: 21 = 3 times 7, composite. Option C: 25 = 5 times 5 and 27 = 3 times 9, both composite. Option D: 33 = 3 times 11 and 35 = 5 times 7, both composite. Only option A contains two prime numbers.

The answer is True. The divisibility rule for 5 states that any number ending in 0 or 5 is a multiple of 5. For example 25, 35, 50, and 85 all end in 0 or 5 and are all divisible by 5. This means any number ending in 0 or 5 is automatically composite unless it equals 5 itself.

A prime number has exactly two factors: 1 and itself. 11 is divisible only by 1 and 11, making it prime. Option A: 9 = 3 times 3. Option C: 15 = 3 times 5. Option D: 21 = 3 times 7. All three have more than two factors and are composite.

5 has factors 1 and 5 only, confirming A. 7 has factors 1 and 7 only, confirming C. 11 has factors 1 and 11 only, confirming D. Option B: 6 has factors 1, 2, 3, and 6, giving it four factors, making it composite. Numbers with exactly two factors are by definition prime numbers.

85 ends in 5, and any number ending in 0 or 5 is divisible by 5. Verified: 85 divided by 5 = 17 exactly. Option A: 85 is odd so not divisible by 2. Option B: digit sum 8+5=13, not a multiple of 3. Option D: 85 divided by 7 = 12 remainder 1. Only 5 divides 85 exactly by the last-digit rule.

The answer is True. All natural numbers greater than 1 fall into exactly one of two categories. If a number has exactly two factors it is prime, and if it has more than two factors it is composite. The number 1 is the only exception — it has only one factor and belongs to neither category.

2 is the smallest prime because it has exactly two factors, 1 and 2. Option A: 1 has only one factor and is neither prime nor composite. Options C and D are prime but are larger than 2. The number 2 is also the only even prime.

The answer is True. Every even number greater than 2 is divisible by 2 in addition to 1 and itself, giving it at least three factors. Having more than two factors means it cannot be prime and must be composite. The only even prime is 2 itself.

The answer is True. 2 has exactly two factors, 1 and 2, satisfying the definition of prime. Every other even number is divisible by 2 in addition to 1 and itself, giving it at least three factors and making it composite. No other even number can ever be prime.

84 = 2 times 2 times 3 times 7. The prime factors are 2, 3, and 7. Option C gives 3, which is prime and divides 84 exactly. Option A gives 4 = 2 times 2, which is composite. Option B gives 6 = 2 times 3, also composite. Option D gives 21 = 3 times 7, also composite. Only 3 is both a factor of 84 and a prime number.

13 is divisible only by 1 and 13, confirming A. 17 is divisible only by 1 and 17, confirming C. 19 is divisible only by 1 and 19, confirming D. Option B: 14 = 2 times 7, giving it four factors, making it composite.

Digit sum = 5 + 7 = 12. Since 12 is a multiple of 3, the number 57 is divisible by 3 and therefore composite. Option A gives 10, option B gives 11, option D gives 13, none of which match the actual digit sum of 57.

44 is even, 45 has digit sum 9 making it divisible by 3, and 46 is even. 47 is odd, not divisible by 3 (digit sum 11), not divisible by 5, and not divisible by 7 (7 times 6 = 42, 7 times 7 = 49). 47 has no factors other than 1 and 47, making it the next prime after 43.

21 = 3 times 7, giving it four factors: 1, 3, 7, and 21. Having more than two factors makes it composite. Option A: 17 is prime with only factors 1 and 17. Option B: 19 is prime. Option D: 23 is prime. Only 21 has factors other than 1 and itself.

46 ends in 6, making it even and immediately divisible by 2. Any even number greater than 2 is composite. Option B: 49 is odd. Option C: 51 is odd. Option D: 55 is odd. Only 46 fails the divisibility-by-2 test and is immediately eliminated as a prime candidate.

A composite number has more than two factors. For example 12 has factors 1, 2, 3, 4, 6, and 12. Option A is incorrect — prime numbers have exactly two factors. Options C and D name mathematical concepts unrelated to classifying numbers by factor count.

27: digit sum 2+7=9, a multiple of 3, confirming A. 42: digit sum 4+2=6, a multiple of 3, confirming C. 75: digit sum 7+5=12, a multiple of 3, confirming D. Option B: 34 has digit sum 3+4=7, not a multiple of 3, so 34 is not divisible by 3.

49 is odd, passing the 2 test. Digit sum 4+9=13 is not a multiple of 3, passing the 3 test. It does not end in 0 or 5, passing the 5 test. Option B: 45 ends in 5, failing the 5 test. Option C: 50 ends in 0, failing the 5 test. Option D: 42 is even, failing the 2 test. Only 49 passes all three tests.

The answer is False. 49 = 7 times 7, giving it three factors: 1, 7, and 49. A prime number must have exactly two factors. Since 49 has a factor of 7 in addition to 1 and itself, it is composite. 49 is a common trap because it is not divisible by 2, 3, or 5, but it fails the divisibility-by-7 check.