A Prime factor is a factor that is a prime number. As we know, a prime number can only be divided by itself and 1. Therefore a prime number has exactly two factors these are one and the number. For example 5 is a prime number because its factors are only 1 and 5. Note that 1 is not a prime factor because it has only one factor not two. 8 is not a prime number because it has more than two factors; 1, 2, 4 and 8. However, among the factors of 8 (1, 2, 4 and 8) 2 is a prime number therefore 2 is a prime factor of 8.The factors of 18 are {1, 2, 3, 6, 9 and 18.} 2 and 3 are prime numbers therefore 2 and 3 are the prime factors of 18
Lesson Content
A product of primes has only prime numbers in it multiplication. For example, 20 expressed as a product of its prime factors is 2×2×5 = 20
Now if a number is broken down into factors which are prime numbers then the number is said to have been expressed as a product of its prime factors.
Note that every composite number can be written as a product of its prime factors
When a number is given as a product of its prime factors, it is said to be factorized completely. A prime factor tree is a special diagram where you find the factors of a number until you can’t factorise any more. The result is all the prime factors of the number.
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