Prime Factorization
Prime factorization is the process of breaking down a number into its prime factors
Prime factorization is the process of breaking down a number into its prime factors. Prime factors are the prime numbers that, when multiplied together, equal the original number.
To find the prime factorization of a number, follow these steps:
1. Start by dividing the 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 on to the next prime number, which is 3.
2. Divide the number by 3. If it is divisible, then 3 is a prime factor. If not, continue with the next prime number, which is 5.
3. Repeat this process with increasing prime numbers until all the prime factors have been found.
4. Continue dividing the number by prime numbers until the quotient is 1.
5. Write down all the prime factors obtained in the previous steps. The prime factorization of the original number is the product of these prime factors.
Let’s walk through an example to illustrate the process:
Example: Find the prime factorization of 48.
1. Divide 48 by 2. It is divisible, so 2 is a prime factor. The quotient is 24.
48 ÷ 2 = 24
2. Divide 24 by 2. It is divisible, so 2 is a prime factor. The quotient is 12.
24 ÷ 2 = 12
3. Divide 12 by 2. It is divisible, so 2 is a prime factor. The quotient is 6.
12 ÷ 2 = 6
4. Divide 6 by 2. It is divisible, so 2 is a prime factor. The quotient is 3.
6 ÷ 2 = 3
5. Since 3 is a prime number, we have found all the prime factors. The quotient is 1.
The prime factors of 48 are 2, 2, 2, and 3.
So, the prime factorization of 48 is 2 * 2 * 2 * 3, which can also be written as 2^3 * 3.
More Answers:
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