Prime numbers have exactly two factors, one and itself. Composite numbers have more than two factors. Prime factorization is breaking a number down into its prime factors. Examples show finding the prime factors of numbers like 36, 108, 120, and 144 using factor trees or division by primes. Every number has a unique prime factorization.

2. Lets Learn!
A prime number has exactly two factors, one and itself.
A composite number has more than two factors.
One is neither prime nor composite. It only has itself as a factor.
Two is the only even prime number.
The method in finding prime number is called prime factorization.

3. The following are examples of prime numbers and
composite number.
Prime Numbers Factors
3 1 and 3
5 1 and 5
13 1 and 13
29 1 and 29
31 1 and 31
Composite Numbers Factors
4 1, 2, and 4
6 1, 2, 3 and 6
8 1, 2, 4 and 8
9 1, 3 and 9
12 1, 2, 3, 4, 6 and 12

4. Prime Factorization
Prime factorization is when you break a number down into its prime
factors.
The prime factorization of a number is the product of primes that
make up that number.
Every number has a unique prime factorization.
Factor tree and division by primes are one of the methods in finding
prime factors.

5. Example 1. Find the prime factors of 36 using factor tree.
1. Start with any two factors.
2. Continue finding factors until you
reach all prime factors of the given
number.
So, the prime factor of 36 is
3 x 3 x 2 x 2 or 32 x 22.

6. Example 2. Find the prime factors of 108 using factor tree.
The prime factor of 108 is
2 x 2 x 3 x 3 x 3 or 22 x 33.

7. Example 3. Find the prime factors of 120 using division by
prime method.
So, the prime factor of 120 is
2 x 2 x 2 x 3 x 5 or 23 x 3 x 5.

8. Example 4. Find the prime factors of 144 using division by
prime method.
The prime factor of 144 is
2 x 2 x 2 x 2 x 3 x 3 or 24 x 33.