**Prime Factorization**

**Prime Factorization**

A **prime number **is a number that has exactly two factors i.e. 1 and the number itself.

Eg: 3 is a prime number because 3 can be divided by only two numbers i.e. 1 and 3 itself. In the same way, 2, 5, 7, 11, 13, and 17 are prime numbers.

A **composite number** has more than two factors, which means apart from getting divided by 1 and the number itself.

Eg: 12 is a composite number because it can be divided by 1, 2, 3, 4, 6 and 12. So, the number ‘12’ has 6 factors.

**Twin primes and co-prime**

Two prime numbers are called twin primes if there is present only one composite number between them. Or we can also say two prime numbers whose difference is two are called twin primes.

Eg: {3, 5}, {5, 7}, {11, 13}, {17, 19}, {29, 31}, {41, 43}

Co-prime numbers are pairs of numbers that do not have any common factor other than 1.

**Prime factorization:**

Prime factorization is a way of expressing a number as a product of its prime factors.

There are different ways to find prime factors:

**a) Factor Tree Method:**

We write pairs of factors for the given number in circles which make branches of a factor tree.

To find the prime factorization of the given number using the factor tree method, follow the below steps:

Step 1: Consider the given number as the top of the tree

Step 2: Write down the first pair of factors of that number as the branches of a tree

Step 3: Check if the numbers can be further divided.

Step 4: If yes, again factorize the composite factors, and write down the factors pairs as the branches

Step 5: Repeat the step, until no factor can be further divided. The last numbers are the prime factors of the given composite factors.

** b) Division Method:**

Step 1: Divide the given number by the smallest prime number. …

Step 2: Again, divide the quotient by the smallest prime number.

Step 3: Repeat the process, until the quotient becomes 1.

Step 4: Finally, multiply all the prime factors.

**Math facts:**

– 1 is not a prime number.

**Different ways of teaching:**

Teaching through stories: