Prime Factorization Calculator

How to Calculate Prime Factorization

Prime factorization is the process of breaking down a number into the product of its prime factors. This is a fundamental concept in number theory and has various applications in mathematics and computer science.

Formula

There isn't a single formula for prime factorization, but the process can be described as:

\[ n = p_1^{a_1} \times p_2^{a_2} \times ... \times p_k^{a_k} \]

Where:

• n is the number being factored
• p₁, p₂, ..., pₖ are prime numbers
• a₁, a₂, ..., aₖ are positive integers

Calculation Steps

1. Start with the number you want to factor.
2. Find the smallest prime number that divides evenly into your number.
3. Divide your number by this prime number.
4. Repeat steps 2 and 3 with the quotient until the quotient itself is a prime number.
5. The prime factors are all the prime numbers you divided by, including the final quotient if it's greater than 1.

Example

Let's find the prime factorization of 84:

1. Start with 84
2. The smallest prime factor of 84 is 2: \[ 84 \div 2 = 42 \]
3. 42 is even, so we divide by 2 again: \[ 42 \div 2 = 21 \]
4. 21 is odd, the next prime factor is 3: \[ 21 \div 3 = 7 \]
5. 7 is prime, so we stop here

Therefore, the prime factorization of 84 is: 2 × 2 × 3 × 7, or 2² × 3 × 7

Visual Representation

This diagram illustrates the prime factorization process for 84, showing how it breaks down into its prime factors.