How to Write a Number as a Product of Its Prime Factors?

To write a number as a product of its prime factors, you repeatedly divide the number by prime numbers until you are left with 1. Then, you express the original number as the product of all the prime divisors you used.

Here's a breakdown of the process:

1. Start with the number you want to factorize.

2. Find the smallest prime number that divides the number evenly. A prime number is a whole number greater than 1 that has only two divisors: 1 and itself (e.g., 2, 3, 5, 7, 11).

3. Divide the number by that prime number.

4. If the result is a prime number, you're done!

5. If the result is not a prime number, repeat steps 2-4 with the result of the division, until you reach a prime number.

6. Express the original number as the product of all the prime factors you found.

Let's illustrate with examples:

Example 1: Prime factorization of 30

• 30 is divisible by 2 (a prime number). 30 / 2 = 15
• 15 is divisible by 3 (a prime number). 15 / 3 = 5
• 5 is a prime number.

Therefore, 30 = 2 x 3 x 5

Example 2: Prime factorization of 28

• 28 is divisible by 2 (a prime number). 28 / 2 = 14
• 14 is divisible by 2 (a prime number). 14 / 2 = 7
• 7 is a prime number.

Therefore, 28 = 2 x 2 x 7 = 2² x 7

Example 3 (Using the "Tree" Method, as hinted in the reference):

Let's factorize 60:

• We can split 60 into 6 x 10
• 6 can be split into 2 x 3 (Both 2 and 3 are prime, so we circle them)
• 10 can be split into 2 x 5 (Both 2 and 5 are prime, so we circle them)

Therefore, 60 = 2 x 2 x 3 x 5 = 2² x 3 x 5

Key Considerations:

• Always start with the smallest prime number (2) and work your way up.
• Continue factoring until all factors are prime numbers.
• You can use a "factor tree" to visually represent the prime factorization process.
• Expressing the prime factorization using exponents is optional but can be helpful when dealing with larger numbers or repeated prime factors.