Identifying Prime & Composite Numbers

1. Identify whether 79 is a prime or composite number. Justify your answer.
2. Which of the following numbers is composite: 37, 45, 53, 61?
3. Identify the smallest composite number and explain why it is composite.
4. List all prime numbers between 20 and 50.
5. A number has exactly three factors. Can it be prime? Explain why or why not.
6. Find the prime factorization of 84 using a factor tree.
7. Write the prime factorization of 126 using division.
8. If a number’s prime factorization is 2 × 3 × 5, what is the number?
9. Two numbers have the same prime factors but different values. What could these numbers be?
10. A number is a multiple of both 7 and 11. Is it necessarily prime? Why or why not?
11. Find the smallest prime number that is greater than 90.
12. Find a two-digit composite number that is a multiple of two different prime numbers.
13. If a number is divisible by 3 and 5, is it always composite? Justify your answer.
14. The product of two prime numbers is 51. Find the numbers.
15. A number is divisible by both 2 and 3. Can it be prime? Why or why not?
16. Test if 91 is prime using divisibility rules.
17. If a number has exactly four factors, can it be prime? Explain.
18. Find a prime numbers between 70 and 100.
19. A number is divisible by 7 but not by 2 or 3. Can it be prime?
20. Find the smallest three-digit composite number.
21. A number is composite and has only two prime factors. Find such a number between 40 and 60.
22. List three composite numbers whose sum is 72.
23. A composite number is greater than 50 and has exactly four factors. Find the number.
24. A shopkeeper packs 24 chocolates in boxes of equal numbers. If each box contains a composite number of chocolates, what are the possible values?
25. A teacher arranges 49 students in rows of equal numbers. If each row has a prime number of students, what are the possible row arrangements?
26. A number is the product of two consecutive prime numbers and is between 50 and 80. Find the number.
27. A number is made by multiplying three different prime numbers and is between 90 and 150. Find the number.
28. Find the number which has all the prime numbers from 1 to 10 as factors.