Factors of 30 | Prime Factorization of 30 - Explained Simply
Today we are going to present here Factor Tree of 30. The factor is the number that divides the original number. The Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30 itself.
What are the factors of 30?
To find the factors of 30, we look for all the whole numbers that can divide 30 evenly without leaving a remainder.
Factor Tree Method of 30: Explained Simply
Step 1: Start checking from 1.
1 divides 30 (1 × 30 = 30). So, 1 and 30 are factors.
Step 2: Check 2.
2 divides 30 (2 × 15 = 30). So, 2 and 15 are factors.
Step 3: Check 3.
3 divides 30 (3 × 10 = 30). So, 3 and 10 are factors.
Step 4: Check 4.
4 does not divide 30 evenly (30 divided by 4 is 7 with a remainder of 2). So, 4 is not a factor.
Step 5: Check 5.
5 divides 30 (5 × 6 = 30). So, 5 and 6 are factors.
Step 6: Check 6.
We have already found 6 as a factor when we paired it with 5. Since we have reached a number that has already been identified as a factor in a pair, we have found all unique factors.
Listing all the unique factors in ascending order gives us: 1, 2, 3, 5, 6, 10, 15, 30.
Prime Factorization of 30
Now, let's apply these definitions to our target number: 30. Thirty is a composite number because it has more than two factors (its factors are 1, 2, 3, 5, 6, 10, 15, and 30). We want to find the prime numbers that multiply together to make 30.
There are a couple of popular methods to achieve this: the Factor Tree Method and the Division Method.
The Factor Tree of 30
The factor tree is a visual and intuitive way to find prime factors.
Start with the number at the top:
```
30
```
Break it down into any two factors: Think of any two numbers that multiply to give you 30. Let's start with 3 and 10.
```
30
/ \
3 10
```
Identify prime factors and circle them: Is 3 a prime number? Yes! Circle it. Is 10 a prime number? No, it's composite.
```
30
/ \
(3) 10
```
Continue breaking down composite numbers: Now, take 10 and break it down into two factors. For example, 2 and 5.
```
30
/ \
(3) 10
/ \
2 5
```
Circle all new prime factors: Are 2 and 5 prime numbers? Yes, both are. Circle them.
```
30
/ \
(3) 10
/ \
(2) (5)
```
Collect all the circled prime numbers: Once all the branches of your tree end in circled prime numbers, you're done! The prime factors of 30 are 2, 3, and 5.
So, the prime factorization of 30 is: 2 × 3 × 5
What if you started with different factors? Let's say you started with 6 and 5:
```
30
/ \
6 (5)
/ \
(2) (3)
```
You still end up with (2), (3), and (5)! This demonstrates the uniqueness of prime factorization.
The Division Method of 30 (Ladder Method)
This method is more structured and involves repeatedly dividing the number by the smallest possible prime number until you can't divide anymore.
Start with the number and divide by the smallest prime number: The smallest prime number is 2. Does 2 divide 30 evenly? Yes, 30 ÷ 2 = 15.
```
2 | 30
|15
```
Now take the result (15). Can it be divided by 2? No, it's odd. What's the next smallest prime number? 3. Does 3 divide 15 evenly? Yes, 15 ÷ 3 = 5.
```
2 | 30
3 | 15
|5
```
Repeat until the result is a prime number (or 1): Now take the result (5). Can it be divided by 3? No. What's the next smallest prime number? 5. Does 5 divide 5 evenly? Yes, 5 ÷ 5 = 1.
```
2 | 30
3 | 15
5 | 5
|1
```
Collect the prime divisors:
The prime numbers you used to divide (the numbers on the left side of the ladder) are your prime factors.
So, the prime factorization of 30 is: 2 × 3 × 5
Both methods yield the same result, confirming the unique prime factorization of 30.