# Product of Prime Factors

What will you do if you have to write a natural number as a product of prime factors? This video explains how to do just that with the use of two methods. The first method is known as the tree diagram and is more commonly used in primary school, while the second method is known as the ladder method and is more commonly used in high school.

Method 1: If you have the number 12, you can write it in terms of the factor pair of 3 times 4. As 3 is a prime number, you stop at that branch, but, as 4 is not a prime number, you need to write a factor pair for 4. So, as 2 times 2 is a factor pair of 4 and 2 is a prime number, you will also stop with that branch. Thus, 12 written as the product of prime factors will be 3 x 2 x 2. Or you can write it as 2 x 2 x 3 which will be 2 squared times 3.

Method 2: When doing the ladder method, always check the prime numbers in ascending order, starting with your smallest prime number, 2. Can 12 be divided by 2? Yes, 2 can go into 12 six times. Continue with the 2. Can 6 be divided by 2? Yes, 6 divided by 2 is 3. Can 2 go into 3? No. Go on to the next prime number, namely 3. Can 3 be divided by 3? Yes, and as 3 is also a prime number, you stop with the ladder. Thus, 12 written as a product of prime factors will be 2 x 2 x 3.