How do you find the prime factor of a number?
The process of writing a number as the product of prime numbers is prime factorization.
Answer: The prime factors of a number can be found with the help of the division method or the factor tree method.
We have two ways to prime factorize numbers.
- Factor tree method
- Division method
Method 1: Prime factorization using the factor tree method
In the factor tree method, the factors of a number are found and then those numbers are further factorized until we reach the prime numbers. To do the prime factorization of a number using the factor tree method, follow the steps given below:
- Step 1: Factorize the given number and write down the pair of factors as the next branches of the tree.
- Step 2: Repeat the steps, until we get the prime factors of all the composite factors.
Example: Find the prime factors of 225 using the factor tree method.
Method 2: Division method
The division method can also be used to find the prime factors of a large number by dividing the number by prime numbers. Follow the steps given below to find the prime factors of a number by using the division method:
- Step 1: Divide the number by the smallest prime number such that the smallest prime number should divide the number completely.
- Step 2: Again, divide the quotient of step 1 by the smallest prime number.
- Step 3: Repeat step 2, until the quotient becomes 1.
- Step 4: Finally, multiply all the prime factors that are the divisors of the division.
Example: Find the prime factors of 225 using the division method.