Question

What is the prime factor tree for 200?

Answer 1

Hint: We need to obtain the prime factors of 200 which is a composite number. We need to do this by dividing the number 200 by the smallest prime number possible which can divide the number. We repeatedly do this till we get the final prime number. If it is not a prime number, we keep dividing till we obtain prime numbers.

Complete step by step answer:
In order to solve this question, let us first divide the number 200 by the smallest prime number which is 2 which can divide 200 completely. This gives us 100. Next, we divide this by a smallest prime number again which is 2. This gives us 50. We repeat this till we get all the factors as prime. Next, we again try to divide this number 50 by 2 which gives us 25. Next, if we try to divide this by 2, we cannot divide them. Hence, we go for the next smallest prime number which can divide 25 which is 5. This gives us 5. We stop now since we have obtained a prime number.
Now, we need to represent this in the form of a tree as shown below.

Hence, we have drawn the prime factor tree for 200.

Note: We need to note that the tips of the tree always end with a prime number. We need to be careful to choose only the smallest prime number that can divide the number at any stage. Otherwise, it will not give us a correct prime factor tree.