Complete the factor tree with whole numbers to create a factor tree for 72. (2 points)

Question

Remaining Attempts : 3

Answer 1

To create a factor tree for the number 72, we can start by dividing it by the smallest prime number:

1. Start with 72:

   • Divide 72 by 2 (the smallest prime number): \[ 72 \div 2 = 36 \]
   • So, we write: 72 = 2 × 36

2. Next, we take 36 and factor it further:

   • Divide 36 by 2: \[ 36 \div 2 = 18 \]
   • So, we write: 36 = 2 × 18
   • Now we have: 72 = 2 × 2 × 18

3. Next, we take 18 and factor it further:

   • Divide 18 by 2: \[ 18 \div 2 = 9 \]
   • So, we write: 18 = 2 × 9
   • Now we have: 72 = 2 × 2 × 2 × 9

4. Finally, we can factor 9:

   • Divide 9 by 3 (the next smallest prime number): \[ 9 \div 3 = 3 \]
   • So, we write: 9 = 3 × 3
   • Now we have: 72 = 2 × 2 × 2 × 3 × 3

So the complete factor tree for 72 is: \[ 72 \rightarrow 2 \quad (36) \rightarrow 2 \quad (18) \rightarrow 2 \quad (9) \rightarrow 3 \quad (3) \]

In prime factorization form, 72 can be expressed as: \[ 72 = 2^3 \times 3^2 \]