Express each number as a product of its prime factors
5005

Answer

To express the number 5005 as a product of its prime factors, we can follow these steps:

### Step 1: Start with the number 5005.
We need to factorize this number into its prime components.

### Step 2: Check for divisibility by the smallest prime number, which is 2.
5005 is an odd number, so it is not divisible by 2.

### Step 3: Check for divisibility by the next smallest prime number, which is 3.
To check for divisibility by 3, we can sum the digits of 5005:
5 + 0 + 0 + 5 = 10.
Since 10 is not divisible by 3, 5005 is also not divisible by 3.

### Step 4: Check for divisibility by the next prime number, which is 5.
Since 5005 ends with a 5, it is divisible by 5.
5005 ÷ 5 = 1001.

### Step 5: Now factor 1001.
Next, we need to factor 1001. We will check for divisibility by the next smallest prime numbers.

### Step 6: Check for divisibility by 7.
1001 ÷ 7 = 143 (since 1001 is divisible by 7).

### Step 7: Now factor 143.
Next, we need to factor 143.

### Step 8: Check for divisibility by 11.
143 ÷ 11 = 13 (since 143 is divisible by 11).

### Step 9: Now we have reached a prime number.
The number 13 is a prime number.

### Step 10: Combine all the factors.
Now we can express 5005 as a product of its prime factors:
5005 = 5 × 7 × 11 × 13.

### Final Answer:
Thus, the prime factorization of 5005 is:
**5005 = 5 × 7 × 11 × 13.**

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