Identifying Prime Numbers

1) Which of these is the set of prime numbers?

{2, 3, 5, 7}

{4, 6, 8, 9}

{10, 12, 14, 15}

{2, 4, 6, 8}

The only set that contains only primes is {2, 3, 5, 7}.

Explanation

The only set that contains only primes is {2, 3, 5, 7}.

2) Which of these pairs are both prime?

14 and 15

17 and 19

20 and 22

25 and 27

17 and 19 are both primes. The other pairs contain composite numbers.

Explanation

17 and 19 are both primes. The other pairs contain composite numbers.

3) Which number is a prime less than 20?

18

19

20

21

19 is prime. 18, 20, and 21 are composite.

Explanation

19 is prime. 18, 20, and 21 are composite.

4) Is 23 prime or composite?

Neither prime nor composite

Prime

Composite

Even composite

23 has only two factors (1 and 23), so it is prime.

Explanation

23 has only two factors (1 and 23), so it is prime.

5) Prime factorization of 36 is:

3 × 12

6 × 6

2 × 2 × 3 × 3

4 × 9

36 = 2 × 2 × 3 × 3. Only this option shows prime factors.

Explanation

36 = 2 × 2 × 3 × 3. Only this option shows prime factors.

6) Which number is not prime?

31

33

37

41

33 = 3 × 11, so it is composite. The others are prime.

Explanation

33 = 3 × 11, so it is composite. The others are prime.

7) Which number is composite?

12

13

17

19

12 has many factors (1, 2, 3, 4, 6, 12), so it is composite. 13, 17, and 19 are prime.

Explanation

12 has many factors (1, 2, 3, 4, 6, 12), so it is composite. 13, 17, and 19 are prime.

8) Which of the following is a prime number?

9

15

11

21

Prime numbers have only two factors: 1 and themselves.

11 is prime, while 9 = 3×3, 15 = 3×5, and 21 = 3×7 are composite.

Explanation

Prime numbers have only two factors: 1 and themselves.

11 is prime, while 9 = 3×3, 15 = 3×5, and 21 = 3×7 are composite.

9) Which is true about 97?

It is prime.

It is composite.

It is an even prime.

It is neither.

97 is prime because its only factors are 1 and 97.

Explanation

97 is prime because its only factors are 1 and 97.

10) What is the smallest prime number?

0

1

2

3

The number 1 is not prime, and 0 is not prime. The smallest prime is 2, which is also the only even prime.

Explanation

The number 1 is not prime, and 0 is not prime. The smallest prime is 2, which is also the only even prime.

11) What is the prime factorization of 20?

2 × 10

2 × 2 × 5

4 × 5 × 1

20 × 1

Breaking down 20 into primes: 20 = 2 × 2 × 5. That’s the prime factorization.

Explanation

Breaking down 20 into primes: 20 = 2 × 2 × 5. That’s the prime factorization.

12) Which number is composite?

41

43

45

47

45 = 3 × 15, so it is composite. The others are prime.

Explanation

45 = 3 × 15, so it is composite. The others are prime.

13) Which statement is true?

All odd numbers are prime.

2 is the only even prime.

1 is a prime number.

9 is a prime number.

The only even prime is 2. Most odd numbers are not prime (like 9, 15). Also, 1 is neither prime nor composite.

Explanation

The only even prime is 2. Most odd numbers are not prime (like 9, 15). Also, 1 is neither prime nor composite.

14) The next prime after 43 is:

44

45

46

47

44, 45, and 46 are composite. The next prime is 47.

Explanation

44, 45, and 46 are composite. The next prime is 47.

15) Which number is prime?

21

25

29

33

29 is prime because its only factors are 1 and 29. 21, 25, and 33 are composite.

Explanation

29 is prime because its only factors are 1 and 29. 21, 25, and 33 are composite.

16) The number 1 is:

Prime

Composite

Neither prime nor composite

Even

By definition, 1 is not considered prime or composite.

Explanation

By definition, 1 is not considered prime or composite.

17) Which of these numbers has exactly two factors?

9

13

15

20

13 has only two factors (1 and 13), so it is prime. The others have more factors.

Explanation

13 has only two factors (1 and 13), so it is prime. The others have more factors.

18) How many prime factors does 30 have?

2

3

4

5

30 = 2 × 3 × 5. It has 3 prime factors.

Explanation

30 = 2 × 3 × 5. It has 3 prime factors.

19) How many factors does 7 have?

1

2

3

4

7 has exactly 2 factors: 1 and 7. That makes it prime.

Explanation

7 has exactly 2 factors: 1 and 7. That makes it prime.

20) Which of the following is a prime number?

51

57

63

59

59 has only two factors (1 and 59), so it is prime. The others are composite.

Explanation

59 has only two factors (1 and 59), so it is prime. The others are composite.