Short Answer 
To factor the number 2457, start by testing divisibility with prime numbers. After confirming that 2457 can be divided by 3 multiple times and then factoring 91 into 7 and 13, the complete prime factorization is 2457 = 3³ x 7 x 13.
Step 1: Understand the Number
To begin factoring the number 2457, it’s crucial to first recognize the properties of the number. Note that it is not divisible by 2 (as it is odd), so we will start testing for divisibility with the next smallest prime number, which is 3. Understanding the prime factors helps streamline the factorization process.
Step 2: Start Factoring with Prime Numbers
Next, you’ll want to systematically check for divisibility starting with 3. Continue testing larger prime numbers until you completely factor 2457. You can follow these checks:
- Check divisibility by 3: 2457 ‚àö‚àë 3 = 819.
- Check divisibility of 819 by 3: 819 ‚àö‚àë 3 = 273.
- Check divisibility of 273 by 3: 273 ‚àö‚àë 3 = 91.
- Now factor 91 into 7 and 13.
Step 3: Write Down the Prime Factorization
Finally, consolidate your findings into the complete prime factorization of 2457. After deriving all factors, express it as a product of prime numbers. The factors you discovered yield:
- 2457 = 3³ x 7 x 13
This shows that 2457 can ultimately be represented as the multiplication of its prime factors. Understanding this method can be beneficial for similar factorization tasks in the future.