Finding Prime Factorization Of A Number
The prime factorization of an integer contains only prime factors. All answers were calculated using the upside down division method. We could have also used other methods such as a factor tree to arrive to the same answer. The method used is not important. What is important is to correctly solve the solution.
List of divisibility rules for finding prime factors faster
Knowing these divisibility rules will help you find prime factors more easily. Finding prime factors faster helps you solve prime factorization faster.
Rule 1: If the last digit of a number is 0, 2, 4, 6 or 8 then it is an even number. All even numbers are divisible by 2 and 2 is a prime factor.
Rule 2: If the sum of digits of a number is divisible by 3 then the number is also divisible by 3 and 3 is a prime factor(example: the digits of 102 are 1, 0 and 2 so 1+0+2=3 and 3 is divisible by 3, meaning that 102 is divisible by 3). The same logic works also for number 9.
Rule 3: If the last two digits of a number are 00 then this number is divisible by 4(example: we know that 212=200+12 and 200 has two zeros in the end making it divisible with 4. We also know that 4 is divisible with 12). In order to use this rule to it's fullest it is best to know multiples of 4.
Rule 4: If the last digit of a number is 0 or 5 then 5 it is divisible by 5 and 5 is a prime factor.
Rule 5: All numbers that are divisible by both 2 and 3 are also divisible by 6.
What Is Prime Factorization Of A Number?
In mathematics breaking down a composite number(a positive integer that can be the sum of two smaller numbers multiplied together) into a multiplication of smaller numbers is called factorization. When the same process is continued until all numbers have been broken down into their prime factor multiplications then this process is called prime factorization.
Using prime factorization we can find all prime factors containing in a number.