Prime Number Formula: Factorization & Sample Questions

Prime numbers are those that have only two factors. In other words, the number that is divisible by number 1 and itself is a prime number. 1 is not a prime nor a composite number. Factorization is the commonly used method to find prime numbers. Example-3,5,2,7 etc. 4 is composite, though, as it is a product (2 2) that both numbers are less than four. Due to the sheer fundamental theorem of arithmetic, every natural number bigger than 1 is either a prime or can be factorised as a product of primes that is distinct up to their order, primes are crucial in number theory.

Key Takeaways- Prime number, Two factors, Composite number, Factorization

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Finding Prime Numbers using Factorization

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Factorization is the common and easy method to find prime numbers. The steps to find a prime number is as mentioned –

• First, find out the factors of given numbers. 
• Check the total number of factors of the given numbers.
• The numbers that have two factors, 1 and itself than these numbers are prime numbers. If the number has more than two factors then it is a prime number.

Example (A) – Take number 17. Is it a prime number or composite number?

Factors of 17 are 1x17

Since 17 has only two factors, it is a prime number.

Example (B) – Take number 35. Is it a prime number or composite number?

Factors of 35 are 1x5x7

Since 35 have more than two factors, it is a composite number and not a prime number.

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Finding Prime Numbers Using Formulas/ Methods

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Some of the methods used for finding Prime factors are as follows.

Method 1

Two consecutive natural and prime numbers as 2 and 3. Other prime numbers can be written as 6n+1 or 6n-1. Here, n is a natural number.

For example

Let the value of n=1,2,3….

6(1)+1 = 7

6(1)-1= 5

6(2) +1 = 13

6(2)-1 = 11

6(3)+1 = 19

6(3)-1= 17

So, the prime numbers are … 5, 7, 11, 13, 17, 19

Method 2

To find prime natural greater than 40. The formula is n²+n+ 41. Here, n is a natural number.

For example

Let the value of n=0, 1,2,3…39

0 + 0+ 41 = 41

1²+ 1+ 41 = 43

2² +2 +41 = 47

3² +3 + 41 = 53

4² + 2 +41 = 59

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Prime Number Formula Rules

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There are some aspects of prime numbers needed to know the prime numbers and formula

• Any number in a unit’s place is not a prime number.
• The only even-prime number is 2
• In the case of large numbers, all the numbers are added together. If the sum of the numbers is divisible by 3, then that is not a prime number.
• Except numbers 2 and 3. The other prime numbers are expressed with the formulas as 6n+1 or 6n-1.

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Things to Remember

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• The numbers that have only two factors are prime numbers.
• The number that is divisible by 1 and itself is a prime number.
• 0 and 1 are neither prime nor composite numbers.
• Factorization is the common and easy method to find prime numbers.
• The only even prime number is 2
• Except numbers 2 and 3. The other prime numbers are expressed with the formulas as 6n+1 or 6n-1.
• To find the prime numbers greater than 40, the formula is n²+n+ 41.

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