Monday, October 8, 2012

Define Prime Factor

Introduction to define prime factor:

The factors are the divisors of number and we can define the prime factor means the factors of numbers are prime. The prime factors are always positive integer and derived by number theory. If we finding the prime factor that process is called as prime factorization. Now we are going to define about prime factor.

Explanation for Define Prime Factor
Define prime factor:

The prime factor is prime numbers of integer that is that prime numbers are considered as factors. The original integer is always combined with prime numbers. We can define the prime factor by exponent like pa that is the large exponent of ‘p’ is ‘a’ and it is divides the original number.

Define prime factorization:

The prime factorization is the process of finding the prime numbers of divisors. For example, consider the number 8 and find out the prime factors.

First list the factors of number 8 is 2 x 4. Here the 2 is prime and 4 are composite. Again find the prime factors of 4 as 2 x 2. Now the prime factors of 8 are 2 x 2 x 2 or 23. The prime factors are represented in powers.

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More about Define Prime Factor

Example problems for define prime factor:

Problem 1: Find out the prime factors of number 20.

Solution:

The given number is 20.

Factors of number 20 are 4 x 5.

The number 5 is prime and the prime factors of 4 are 2 x 2.

Therefore, the prime factors of 20 are 2 x 2 x 5 (or) 22 x 5.

Problem 2: Find out the prime factors of number 36.

Solution:

The given number is 36.

Factors of number 36 are 6 x 6.

Here we are again finding the prime factors as 3 x 2 x 3 x 2.

Therefore, the prime factors of 36 are 2 x 2 x 3 x 3 (or) 22 x 32.

Exercise problems for define prime factor:

1. Find out the prime factors of number 60.

Solution: The prime factors are 2 x 2 x 3 x 5.

2. Find out the prime factors of number 81.

Solution: The prime factors are 3 x 3 x 3 x 3.

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