This worksheet provides a set of numbers for students to practice breaking down into prime factors using tree diagrams.

To find the prime factors of each number, we break them down into smaller numbers until we are left with only prime numbers (numbers that can only be divided by 1 and themselves).

Here is the step-by-step breakdown for each number:

1. Number 28
* 28 is even, so divide by 2: $28 = 2 \times 14$
* 14 is even, so divide by 2: $14 = 2 \times 7$
* 7 is a prime number.
* Prime Factors: $2, 2, 7$ (or $2^2 \times 7$)

2. Number 65
* 65 ends in 5, so divide by 5: $65 = 5 \times 13$
* 5 is prime.
* 13 is prime.
* Prime Factors: $5, 13$

3. Number 9
* Divide by 3: $9 = 3 \times 3$
* 3 is prime.
* Prime Factors: $3, 3$ (or $3^2$)

4. Number 24
* 24 is even, so divide by 2: $24 = 2 \times 12$
* 12 is even, so divide by 2: $12 = 2 \times 6$
* 6 is even, so divide by 2: $6 = 2 \times 3$
* 3 is prime.
* Prime Factors: $2, 2, 2, 3$ (or $2^3 \times 3$)

5. Number 96
* 96 is even, so divide by 2: $96 = 2 \times 48$
* 48 is even, so divide by 2: $48 = 2 \times 24$
* From before, we know $24 = 2 \times 2 \times 2 \times 3$.
* So, $96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3$.
* Prime Factors: $2, 2, 2, 2, 2, 3$ (or $2^5 \times 3$)

6. Number 51
* Check divisibility by 3 (sum of digits $5+1=6$, which is divisible by 3): $51 = 3 \times 17$
* 3 is prime.
* 17 is prime.
* Prime Factors: $3, 17$

7. Number 35
* Ends in 5, so divide by 5: $35 = 5 \times 7$
* 5 is prime.
* 7 is prime.
* Prime Factors: $5, 7$

8. Number 18
* 18 is even, so divide by 2: $18 = 2 \times 9$
* From before, we know $9 = 3 \times 3$.
* Prime Factors: $2, 3, 3$ (or $2 \times 3^2$)

9. Number 27
* Divide by 3: $27 = 3 \times 9$
* From before, we know $9 = 3 \times 3$.
* So, $27 = 3 \times 3 \times 3$.
* Prime Factors: $3, 3, 3$ (or $3^3$)

Final Answer:
28: $2 \times 2 \times 7$
65: $5 \times 13$
9: $3 \times 3$
24: $2 \times 2 \times 2 \times 3$
96: $2 \times 2 \times 2 \times 2 \times 2 \times 3$
51: $3 \times 17$
35: $5 \times 7$
18: $2 \times 3 \times 3$
27: $3 \times 3 \times 3$