Question 1

What is prime factorization?

Accepted Answer

Prime factorization is the mathematical process of determining which prime numbers multiply together to make the original number. Think of it as breaking down a composite number into its smallest irreducible building blocks. For example, the prime factorization of 12 is 2 × 2 × 3.

Question 2

What is a prime number?

Accepted Answer

A prime number is a whole number greater than 1 whose only divisors are 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, and 17. The number 2 is the only even prime number.

Question 3

What is the Fundamental Theorem of Arithmetic?

Accepted Answer

This theorem states that every integer greater than 1 either is prime itself or is the product of a unique set of prime numbers. This means every number has one, and exactly one, prime factorization representation (ignoring the order of factors).

Question 4

What is exponential form?

Accepted Answer

Instead of writing down repeated factors (like 2 × 2 × 2 × 3), exponential form groups identical factors using exponents. The previous example becomes 2³ × 3. It is a more compact and readable way to represent large prime factor chains.

Question 5

Can negative numbers have prime factors?

Accepted Answer

In standard arithmetic taught in high school, prime factorization is strictly defined for positive integers greater than 1. Negative numbers can be factored by pulling out a -1 first, but the prime factorization theorem applies specifically to positive integers.

Prime Factorization Calculator

What are Primes?

Building the Factor Tree

Step 1: Divide by 2

Step 2: Ascend through Primes

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