2.1 Write the numbers 24,72 and 144 as the product of their prime factors

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To express the numbers 24, 72, and 144 as the product of their prime factors, we will factor each number step by step.

### Step 1: Factor 24
1. Start with 24.
2. Divide by the smallest prime number, which is 2:
   - $$ 24 \div 2 = 12 $$
3. Divide 12 by 2:
   - $$ 12 \div 2 = 6 $$
4. Divide 6 by 2:
   - $$ 6 \div 2 = 3 $$
5. Now, 3 is a prime number.

So, the prime factorization of 24 is:
$$
24 = 2^3 \times 3^1
$$

### Step 2: Factor 72
1. Start with 72.
2. Divide by 2:
   - $$ 72 \div 2 = 36 $$
3. Divide 36 by 2:
   - $$ 36 \div 2 = 18 $$
4. Divide 18 by 2:
   - $$ 18 \div 2 = 9 $$
5. Now, divide 9 by 3:
   - $$ 9 \div 3 = 3 $$
6. Finally, 3 is a prime number.

So, the prime factorization of 72 is:
$$
72 = 2^3 \times 3^2
$$

### Step 3: Factor 144
1. Start with 144.
2. Divide by 2:
   - $$ 144 \div 2 = 72 $$
3. Divide 72 by 2:
   - $$ 72 \div 2 = 36 $$
4. Divide 36 by 2:
   - $$ 36 \div 2 = 18 $$
5. Divide 18 by 2:
   - $$ 18 \div 2 = 9 $$
6. Now, divide 9 by 3:
   - $$ 9 \div 3 = 3 $$
7. Finally, 3 is a prime number.

So, the prime factorization of 144 is:
$$
144 = 2^4 \times 3^2
$$

### Summary of Prime Factorizations
- $$ 24 = 2^3 \times 3^1 $$
- $$ 72 = 2^3 \times 3^2 $$
- $$ 144 = 2^4 \times 3^2 $$
24 = 2³ × 3¹ 72 = 2³ × 3² 144 = 2⁴ × 3²

2.1 Write the numbers 24,72 and 144 as the product of their prime factors

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