What is prime factorization?

Answer 1

it is when you "factor tree" a number down until it cn non longer be broken down.2 factors of 84 are 4 and 21 because when you multiply them, you get 84. factor 4 down into 2 and 2. factor 21 down into 3 and 7. in this case, the prime factorization is two to the second power times three times seven.

Answer 2

"Prime factorization" is the process of finding which prime numbers (prime factors) you need to multiply together to get a certain number.

Examples:

21 = 3 x 7

10 = 2 x 5

20 = 2 x 2 x 5

60 = 2 x 2 x 3 x 5

(these may also be written as 2*5, 2*2*5, and 2*2*3*5)

By convention, prime factorizations are written with the smallest prime numbers first. For example, we wouldn't write 60 = 3 x 2 x 2 x 5. Some texts prefer to write the answer using exponential notation, so that the final answer would be written as 60 = 2^2 x 3 x 5.

A Prime number is a number that has no factors other than itself and 1, but 1 itself is not regarded as a prime number.

The prime numbers below 30 are thus 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. They can be said to have no prime factorization.

Prime Factors

A factor which is a prime number is called a prime factor.

Every positive integer can be expressed as a product of prime numbers (its prime factorization). Moreover, each positive integer has only one prime factorization.

The prime factors can be found by successive division by prime numbers of increasing value.

EXAMPLE : The prime factorization of 54 is 2 x 3 x 3 x 3

This can be written as 2 x 3^3

The prime factors of 54 are thus 2 and 3.

With large numbers, prime factorization is very time-consuming. If there was a quick way to factorize numbers, then it would be easy to break RSA encryption, which uses prime factors, and thereby intercept secret communications over the internet.

Prime factorization is expressing a number as the product of its prime factors. Example: 210 The prime factors of 210 are 2, 3, 5 and 7. The prime factorization of 210 is 2 x 3 x 5 x 7.

This concept applies to natural numbers.

First you need to know the concept of prime number. A number (other than 1) is prime if it can be divided only by 1 and itself. Examples are 2,3,5,7,11,13,17,19,23 ( There are infinitely many primes.)

if a number is not prime, there are primes than can be multiplied together to get it.

( * means multiply)

For example 4 = 2 * 2; 6 = 2*3 ; 9 = 3 * 3; 10 = 2* 5; 14= 2 * 7 ;15 = 3* 5

Sometimes it takes more than two primes to make the number.

8 = 2 * 2 * 2 ; 12 = 2 * 2 * 3 ; 24 = 2 * 2 *2 * 3 .

There is an important theorem that says that every number is either prime or else is the product of primes. Further, except for the order, there is only one set of primes whose product is some given number. These primes are called the prime factorization of the number. ( Numbers that are multiplied together are called factors.)

The prime factorization is useful in many ways, but one basic use is for finding the greatest common factor and the least common multiple.

All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210.
Prime factorisation is the process of finding prime numbers that when multiplied equal the original number.

Example:

Words:

Say you start with 20. You divide 20 by any number that will have a whole quotient. Let us use 5. 20 divided by 5 is 4. Then you try and divide those numbers. 5 is not divisible by any other numbers making it prime. Do not change the 5. 4 is divisible by 2. 4 divided by 2 is 2. So there for the prime numbers that create 20 when multiplied are 2,2, and 5. To see this process in numbers, see below.

20

5x4

5x2x2

This process is prime factorisation.
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210.
a prime number that can go into a certain number.

for example: the prime factorazations of 399 are 3, 7, 19
Prime factorization is the expression of a number as the product of its prime factors.

2 x 3 x 5 x 7 = 210
Prime factorization is the expression of a number as the product of its prime factors.

2 x 3 x 5 x 7 = 210

Answer 3

Prime factors are factors that are prime numbers. Example;

The factors of 12 is 1, 2, 3, 4, 6 and 12.

The prime factor of 12 would be 2 and 3 because they are the only prime numbers in the factor.

This is edited by someone else. This is not by her.

Answer 4

it is when you "factor tree" a number down until it cn non longer be broken down.2 factors of 84 are 4 and 21 because when you multiply them, you get 84. factor 4 down into 2 and 2. factor 21 down into 3 and 7. in this case, the prime factorization is two to the second power times three times seven.

Answer 5

It means to divide an integer into smaller and smaller factors, until each factor is a prime number - that is, until each factor can't be divided into smaller factors any more.