Using the Division Method to Find Prime Factors

The division method is a simple and efficient technique used to find the prime factors of a given number. It involves dividing the number repeatedly by prime numbers until the quotient becomes 1. The prime numbers that are used to divide the given number are its prime factors. Let's understand this method step by step:

Step 1: Start with the Smallest Prime Number
- Begin by dividing the given number by the smallest prime number, which is 2. If the number is divisible by 2, then 2 is a prime factor. If not, move to the next step.

Step 2: Proceed with Other Prime Numbers
- If the given number is not divisible by 2, move on to the next prime number, which is 3. Divide the number by 3 and check if it is divisible. If it is, then 3 is a prime factor. If not, proceed to the next step.

Step 3: Continue with Prime Numbers
- Repeat this process for all prime numbers, including 5, 7, 11, and so on, until the quotient becomes 1. If any prime number divides the given number, it is a prime factor.

Step 4: Record the Prime Factors
- Keep a record of all the prime numbers that divided the given number. These prime numbers are the prime factors of the given number.

Step 5: Example
- Let's take an example to illustrate the division method. Consider the number 60.
- Divide 60 by 2, and the quotient is 30.
- Divide 30 by 2 again, and the quotient is 15.
- Divide 15 by 3, and the quotient is 5.
- Finally, divide 5 by 5, and the quotient is 1.
- The prime factors of 60 are 2, 2, 3, and 5.

Using the division method helps us find the prime factors of a given number efficiently. By dividing the number repeatedly by prime numbers, we can quickly determine its prime factors. This method is particularly useful in simplifying fractions and solving problems related to factors and multiples.

Use divison method to find the prime factors of the following numbers