Prime and Composite Numbers

Show your work for each problem.

1.
Which of these numbers is prime?
1. a)
2. b)
3. c)
4. d)
Answer:
is prime because its only factors are and . The others are composite: , , .
2.
Which statement about the number is correct?
1. a) is both prime and composite
2. b) is a prime number
3. c) is a composite number
4. d) is neither prime nor composite
Answer: is neither prime nor composite
has only one factor (itself), so it doesn't meet the definition of prime (exactly two factors) or composite (more than two factors).
3.
What is the smallest prime number?
1. a)
2. b)
3. c)
4. d)
Answer:
is the smallest prime number. It has exactly two factors: and . It's also the only even prime number!
4.
Which of these numbers is composite?
1. a)
2. b)
3. c)
4. d)
Answer:
is composite because it has factors . The numbers , , and are all prime.
5.
Is prime or composite? Type 'prime' or 'composite'.
Answer: prime
is prime. It's not divisible by (it's odd), not by (, not divisible by ). Since , we don't need to check further.
6.
How many prime numbers are there between and ?
Answer: 4
The primes between and are: . That's prime numbers.
7.
What is the next prime number after ?
Answer: 29
, , , , . But has only factors and , so it's prime!
8.
How many factors does the number have?
Answer: 6
The factors of are: . That's factors, so is composite.
9.
Determine if is prime or composite.
Answer: prime
1. What is approximately? 6
2. Is divisible by ? no
3. Is divisible by ? no
4. Is divisible by ? no
5. Is prime or composite? prime
10.
Find all the factors of and determine if it's prime or composite.
Answer: composite
1. Is divisible by ? yes
2. Is divisible by ? If yes, what's ? 18
3. Is divisible by ? If yes, what's ? 12
4. Is divisible by ? If yes, what's ? 9
5. Is divisible by ? If yes, what's ? 6
6. How many factors does have? Is it prime or composite? composite
11.
List all prime numbers between and .
Answer: 23, 29
1. Is prime? (21 = 3 × 7) no
2. Is prime? no
3. Is prime? yes
4. Is prime? no
5. Is prime? no
6. Is prime? yes
12.
Which of the following statements is TRUE?
1. a)All odd numbers are prime
2. b)All prime numbers are odd
3. c)All even numbers greater than are composite
4. d)The number is prime
Answer: All even numbers greater than are composite
Every even number > is divisible by , so it has at least factors (, , itself). is prime (and even). and are odd but composite. .
13.
What is the sum of all prime numbers between and ?
Answer: 60
The primes between and are . Sum: .
14.
Is prime or composite? Show your work.
Answer: composite
1. What is approximately? 9
2. Is divisible by ? no
3. Is divisible by ? no
4. Is divisible by ? no
5. Is divisible by ? What is ? 13
6. Is prime or composite? composite
15.
Express as a product of prime factors.
Answer: 2 * 2 * 3 * 5
1. Is divisible by ? What is ? 30
2. Is divisible by ? What is ? 15
3. Is divisible by ? no
4. Is divisible by ? What is ? 5
5. Is prime? yes
6. Write as a product of primes 2 * 2 * 3 * 5