Determine if the following numbers are prime or composite: 40, 87, 83, 2, 46, 80, 89, 53, 50, 76, 82, and 94. Show the prime factorization for composite numbers.

Step 2: Continue with numbers 40, 87, and 83.

2. 40 $$40 = 2 \times 20 = 2^2 \times 10 = 2^3 \times 5$$ This is a composite number. $$\boxed{40 = 2^3 \times 5 \text{ (Composite)}}$$
3. 87 $$87 = 3 \times 29$$ This is a composite number. $$\boxed{87 = 3 \times 29 \text{ (Composite)}}$$
4. 83 83 is only divisible by 1 and itself. This is a prime number. $$\boxed{83 \text{ (Prime)}}$$

Step 3: Continue with numbers 2, 46, and 80.

5. 2 2 is only divisible by 1 and itself. This is a prime number. $$\boxed{2 \text{ (Prime)}}$$
6. 46 $$46 = 2 \times 23$$ This is a composite number. $$\boxed{46 = 2 \times 23 \text{ (Composite)}}$$
7. 80 $$80 = 2 \times 40 = 2^2 \times 20 = 2^3 \times 10 = 2^4 \times 5$$ This is a composite number. $$\boxed{80 = 2^4 \times 5 \text{ (Composite)}}$$

Step 4: Continue with numbers 89, 53, and 50.

8. 89 89 is only divisible by 1 and itself. This is a prime number. $$\boxed{89 \text{ (Prime)}}$$
9. 53 53 is only divisible by 1 and itself. This is a prime number. $$\boxed{53 \text{ (Prime)}}$$
10. 50 $$50 = 2 \times 25 = 2 \times 5^2$$ This is a composite number. $$\boxed{50 = 2 \times 5^2 \text{ (Composite)}}$$

Step 5: Continue with numbers 76, 82, and 94.

11. 76 $$76 = 2 \times 38 = 2^2 \times 19$$ This is a composite number. $$\boxed{76 = 2^2 \times 19 \text{ (Composite)}}$$
12. 82 $$82 = 2 \times 41$$ This is a composite number. $$\boxed{82 = 2 \times 41 \text{ (Composite)}}$$
13. 94 $$94 = 2 \times 47$$ This is a composite number. $$\boxed{94 = 2 \times 47 \text{ (Composite)}}$$

Step 6: Continue with numbers 67, 32, and 47.

14. 67 67 is only divisible by 1 and itself. This is a prime number. $$\boxed{67 \text{ (Prime)}}$$
15. 32 $$32 = 2 \times 16 = 2^2 \times 8 = 2^3 \times 4 = 2^4 \times 2 = 2^5$$ This is a composite number. $$\boxed{32 = 2^5 \text{ (Composite)}}$$
16. 47 47 is only divisible by 1 and itself. This is a prime number. $$\boxed{47 \text{ (Prime)}}$$

Step 7: Continue with numbers 3 and 9.

17. 3 3 is only divisible by 1 and itself. This is a prime number. $$\boxed{3 \text{ (Prime)}}$$
18. 9 $$9 = 3 \times 3 = 3^2$$ This is a composite number. $$$$