prime factorization of of 19096
Answers
Answer:
What is the prime factorization of the number 19,096?
A:
The prime factors are: 2 x 2 x 2 x 7 x 11 x 31
or also written as { 2, 2, 2, 7, 11, 31 }
Written in exponential form: 23 x 71 x 111 x 311
What is prime factorization?
Prime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.
Finding the prime factors of 19,096
To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.
If it doesn't make sense yet, let's try it...
Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
Let's start by dividing 19,096 by 2
19,096 ÷ 2 = 9,548 - No remainder! 2 is one of the factors!
9,548 ÷ 2 = 4,774 - No remainder! 2 is one of the factors!
4,774 ÷ 2 = 2,387 - No remainder! 2 is one of the factors!
2,387 ÷ 2 = 1,193.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
2,387 ÷ 3 = 795.6667 - This has a remainder. 3 is not a factor.
2,387 ÷ 5 = 477.4 - This has a remainder. 5 is not a factor.
2,387 ÷ 7 = 341 - No remainder! 7 is one of the factors!
341 ÷ 7 = 48.7143 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
341 ÷ 11 = 31 - No remainder! 11 is one of the factors!
31 ÷ 11 = 2.8182 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
31 ÷ 13 = 2.3846 - This has a remainder. 13 is not a factor.
31 ÷ 17 = 1.8235 - This has a remainder. 17 is not a factor.
31 ÷ 19 = 1.6316 - This has a remainder. 19 is not a factor.
Explanation : Mark me as brilliant
2, 2, 2, 7, 11, 31 are the prime factors of 19096