Prime Number Factorization

Introduction to prime numbers factorization:

The process of writing a given number as the product of two or more than two numbers is called factorization of this number.  Multiplication tables help to find the product of any two prime numbers.
For ex:
facorize 3×2=6
when we multiply 3 and 2 to get product 6. One the other side we can start with 6 and can write it as the product 2 and 3 that is 6=2×3. This shows that 3 and 2 are the factors of 6. In other words, 6 has (3×2) factors.

Methods of Prime Numbers Factorization :

In prime factorization a number is written as a product of prime factors is said to in the prime factor form. There are three methods for finding Prime Factorization
Short Division
Prime Factoring
The Tree Method

Short Division Method:
Short division method is used for large numbers factoring with the help of small divisors. By taking small prime (divisors) number divide the large numbers given
Ex:
Find factor 876543

7)81 73 61 51 4 3

1  2   5   2  2  0 remainder =3
Prime Factoring method:
Prime factor method is easy method to find out prime factors by mathematics table with prime number pattern increasing order
Ex:

12 = 2 × 2 × 3
= 22 × 3

So, the prime factors of 12 are 22 and 3.

66 = 2 × 3 × 11
So, the prime factors of 66 are 2, 3 and 11.

I am planning to write more post on prime factorization method, prime factorization factor tree. Keep checking my blog.

Tree method:
Tree method involves branch factor for given numbers from that branch factor divide into another branch of prime number until branch factorize by prime number.
Ex: tree factor for 60

Prime Numbers Factorization - Example Problems

Ex 1: Find prime factorization of 147

Sol:We can't divide 147 evenly by 2, so we try  next prime number, 3:
147 ÷ 3 = 49

Then we  factorize 49, and  7 is only prime number can factorize
49 ÷ 7 = 7
Again 7, we factorize 7 only by 7
147 = 3 × 7 × 7
= 3 × 72
Ex 2: Find  prime factors for 330

Sol:
factors for 2 ¦330
3 ¦165                         
5 ¦55
11¦ 11
2, 3, 5 and 11 can factorize 330
330 = 2 × 3 × 5 × 11

There is no other possible prime numbers  can  multiplied to make 330.

Ex 3: Find prime factorization of 225
Sol:

225 = 32 × 52   are the factors of 225

Ex 4: Find the prime factors of the number 78.

Sol:

Given number = 78

The number 78 should be divided by 2. That is,

78 ÷ 2 = 39

Then, the number 39 should be divided by 3. So we get,

39 ÷ 3 = 13

Since, 78 = 2 × 3 × 13

Therefore, the prime factors of the number 78 will be 2, 3 and 13.