Write all the common prime factors of 720 nad 140.

Explanation

To find the common prime factors of 720 and 140, we will first determine the prime factorization of each number and then identify the common factors.

### Step 1: Prime Factorization of 720
1. Start dividing 720 by the smallest prime number, which is 2.
- \( 720 \div 2 = 360 \)
2. Divide 360 by 2.
- \( 360 \div 2 = 180 \)
3. Divide 180 by 2.
- \( 180 \div 2 = 90 \)
4. Divide 90 by 2.
- \( 90 \div 2 = 45 \)
5. Now, 45 is not divisible by 2, so we move to the next prime number, which is 3.
- \( 45 \div 3 = 15 \)
6. Divide 15 by 3.
- \( 15 \div 3 = 5 \)
7. Finally, 5 is a prime number.

So, the prime factorization of 720 is:
\[ 720 = 2^4 \times 3^2 \times 5^1 \]

### Step 2: Prime Factorization of 140
1. Start dividing 140 by 2.
- \( 140 \div 2 = 70 \)
2. Divide 70 by 2.
- \( 70 \div 2 = 35 \)
3. Now, 35 is not divisible by 2, so we move to the next prime number, which is 5.
- \( 35 \div 5 = 7 \)
4. Finally, 7 is a prime number.

So, the prime factorization of 140 is:
\[ 140 = 2^2 \times 5^1 \times 7^1 \]

### Step 3: Identify Common Prime Factors
Now we will list the prime factors of both numbers:
- Prime factors of 720: \( 2, 3, 5 \)
- Prime factors of 140: \( 2, 5, 7 \)

The common prime factors between 720 and 140 are:
- \( 2 \)
- \( 5 \)

### Final Answer
The common prime factors of 720 and 140 are:
\[ 2 \text{ and } 5 \]

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