Express each number as a product of its prime factors
7429

Answer

To express the number 7429 as a product of its prime factors, we can follow these steps:

### Step 1: Check for divisibility by the smallest prime numbers
We start with the smallest prime numbers: 2, 3, 5, 7, 11, etc.

- **Check divisibility by 2**: 7429 is odd, so it is not divisible by 2.
- **Check divisibility by 3**: The sum of the digits (7 + 4 + 2 + 9 = 22) is not divisible by 3, so 7429 is not divisible by 3.
- **Check divisibility by 5**: The last digit is not 0 or 5, so it is not divisible by 5.
- **Check divisibility by 7**: 7429 ÷ 7 = 1061.2857 (not an integer, so not divisible).
- **Check divisibility by 11**: 7429 ÷ 11 = 675.3636 (not an integer, so not divisible).
- **Check divisibility by 13**: 7429 ÷ 13 = 572.2308 (not an integer, so not divisible).
- **Check divisibility by 17**: 7429 ÷ 17 = 437 (this is an integer, so it is divisible).

### Step 2: Divide by 17
Now that we know 7429 is divisible by 17, we perform the division:

7429 ÷ 17 = 437

### Step 3: Factor 437
Now we need to factor 437. We repeat the process of checking for divisibility:

- **Check divisibility by 2**: 437 is odd, so it is not divisible by 2.
- **Check divisibility by 3**: The sum of the digits (4 + 3 + 7 = 14) is not divisible by 3.
- **Check divisibility by 5**: The last digit is not 0 or 5.
- **Check divisibility by 7**: 437 ÷ 7 = 62.4286 (not an integer).
- **Check divisibility by 11**: 437 ÷ 11 = 39.7273 (not an integer).
- **Check divisibility by 13**: 437 ÷ 13 = 33.6154 (not an integer).
- **Check divisibility by 19**: 437 ÷ 19 = 23 (this is an integer, so it is divisible).

### Step 4: Divide by 19
Now we divide 437 by 19:

437 ÷ 19 = 23

### Step 5: Identify the prime factors
Now we have:

7429 = 17 × 437
437 = 19 × 23

Thus, we can express 7429 as:

7429 = 17 × 19 × 23

### Final Answer
The prime factorization of 7429 is:

**7429 = 17 × 19 × 23**

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