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**.