When you work with numbers, figuring out their prime factors can seem tricky, but it doesn’t have to be. This guide will walk you through how to find the smallest prime factor of a number C in a way that even a 5th grader can easily follow.
Let’s break it down step by step with clear examples and simple explanations.
What is a Prime Factor?
Before we start learning how to find the smallest prime factor of a number C, let’s make sure you understand the basics about prime numbers and prime factors.
A prime number is any number greater than 1 that can only be divided by 1 and itself. In other words, no other numbers can divide it evenly.
Examples of prime numbers: 2, 3, 5, 7, and 11.
A prime factor is just one of those prime numbers that can divide another number perfectly without leaving a remainder.
Why Do We Care About the Smallest Prime Factor?
The smallest prime factor is important because it helps you break down a number into its prime factorization. This is useful for solving math problems, especially in school or when learning about how numbers work in different areas like fractions or number theory.
Steps to Find the Smallest Prime Factor of a Number C
Let’s go through the steps to find the smallest prime factor of any number. For this, we’ll use number C as an example.
Step 1: Check if Number C is Divisible by 2 (The Smallest Prime)
The easiest way to start is by seeing if number C can be divided by 2, the smallest prime number.
- If C is even (like 4, 8, 10), then 2 is the smallest prime factor.
- Example 1: If C = 12, divide it by 2:
12 ÷ 2 = 6. - Since 2 divides 12 evenly, 2 is the smallest prime factor of 12.
Step 2: Check the Next Smallest Primes (3, 5, 7, etc.)
If number C is not divisible by 2, then move on to the next smallest prime numbers: 3, 5, 7, and so on.
- Example 2: If C = 15, start with 2. Since 15 isn’t even, it’s not divisible by 2.
Now, try dividing 15 by 3:
15 ÷ 3 = 5. - Since 3 divides 15 evenly, 3 is the smallest prime factor of (C) that is 15.
Step 3: Use the Square Root Rule for Bigger Numbers
If number C is large, you don’t need to check all numbers. Just check primes up to the square root of C.
- Example 3: If C = 49, the square root of 49 is 7 (because 7 × 7 = 49).
- You only need to check primes up to 7. Start with 2, 3, and 5, but none divide 49 evenly.
- Next, check 7: 49 ÷ 7 = 7.
- So, 7 is the smallest prime factor of 49.
Step 4: If Number C is Prime
If number C can’t be divided evenly by any prime numbers smaller than itself, then C is prime, and its smallest prime factor is C itself.
- Example 4: If C = 13, none of the smaller primes (2, 3, 5, 7, etc.) divide it evenly.
Therefore, 13 is prime, and its smallest prime factor is 13.
Let’s Recap with Another Example
Find the smallest prime factor of number C = 30:
- Start with 2.
30 ÷ 2 = 15, so 2 is the smallest prime factor.
Now, let’s try another number, C = 45:
- Start with 2.
45 ÷ 2 doesn’t work (45 isn’t even). - Next, check 3.
45 ÷ 3 = 15, so 3 is the smallest prime factor of 45.
Key Points to Remember:
- A prime number can only be divided by 1 and itself.
- To find the smallest prime factor, always start with the smallest prime number: 2.
- If 2 doesn’t work, move on to the next primes: 3, 5, 7, etc.
- For bigger numbers, check primes only up to the square root of the number.
- If the number itself is prime, then the smallest prime factor is the number itself.
So, next time someone asks you to find the smallest prime factor of a number, you’ll know exactly what to do. if you have any doubt feel free to ask in the comment section.