Problem 20 - Introductory Algebra for College Students

Question

Identify each natural number as prime or composite. If the number is composite, find its prime factorization. $$100$$

Step-by-Step Solution

Answer

The given number 100 is a composite number and its prime factorization is \(2\times2\times5\times5\) or \(2^2 \times 5^2\).

Step 1: Checking the type of number

The given number is 100. Now, divide 100 by all the natural numbers less than 100 and more than 1. If it is divisible by any number other than 1 and 100, then it is a composite number. Indeed, 100 can be divided evenly by numbers other than 1 and 100 (for example 2, 4, 5, 10, 20, 25), therefore it is a composite number.

Step 2: Finding prime factorization

A prime factorization of the number 100 means to find the prime numbers that multiply together to give the original number, which is 100. Start from the smallest prime number, which is 2. Divide 100 by 2. It is divisible, so write down a 2. Then divide that answer(50) by 2 again, it is divisible, so write down another 2. Repeat this till you get an odd number. Now, divide the last quotient by next prime number which is 3. It is not divisible by 3. So, next we try with the next prime number 5. It is divisible by 5, so write down a 5. Again divide that answer(5) by 5 which gives 1. Once you get 1 as answer, you stop. So the prime factors of 100 are 2, 2, 5, 5.