Decide whether a number is prime or composite, build a factor tree, and express any composite number as a product of its prime factors.
A prime number has exactly 2 factors: 1 and itself. A composite number has more than 2 factors.
A factor tree breaks a number down step by step until every branch ends at a prime number. Those prime numbers, multiplied together, are the prime factorization.
1. Is 7 prime or composite?
Try dividing 7 by 2, 3, 4, 5, 6. None divide evenly. So 7's only factors are 1 and 7 → prime.
2. Which lists the correct prime factorization of 12?
Prime factorization uses only prime numbers. 6 and 4 are not prime, so break them further: 12 = 2 × 6 = 2 × 2 × 3.
3. How many prime factors does 12 have when fully factored? (Count with repetition: 2 × 2 × 3 has three prime factors.)
12 = 2 × 2 × 3. That is three prime factors (two 2s and one 3).
4. What is the largest prime factor in the prime factorization of 18?
18 = 2 × 3 × 3. The prime factors are 2 and 3. The largest is 3.
5. Which number between 10 and 20 is prime?
15 = 3×5 (composite). 18 = 2×9 (composite). 20 = 4×5 (composite). 17 has no factors other than 1 and 17 → prime.
6. The prime factorization of 18 is written as 2 × 3?. What exponent goes on the 3?
18 = 2 × 3 × 3 = 2 × 3². The 3 appears twice, so the exponent is 2.
7. True or false: 9 is a prime number. Choose the correct answer.
9 ÷ 3 = 3, so 3 is a factor of 9. Factors of 9 are 1, 3, 9 — that is 3 factors, so 9 is composite.