Introduction to Prime Factorization
Prime factorization is a fundamental concept in mathematics that helps us understand the building blocks of numbers. It involves breaking down a composite number into a product of prime numbers. In this worksheet, we will explore the concept of prime factorization and provide exercises for 6th-grade students to practice.
What are Prime Numbers?
A prime number is a positive integer that is divisible only by itself and 1. The first few prime numbers are 2, 3, 5, 7, 11, and 13. Prime numbers play a crucial role in prime factorization, as they are the basic units that make up all other numbers.
How to Find Prime Factors
To find the prime factors of a number, we need to identify the prime numbers that multiply together to give the original number. Here are the steps to follow:
- Start by dividing the number by the smallest prime number, which is 2.
- If the number is divisible by 2, write 2 as a factor and divide the number by 2.
- If the number is not divisible by 2, move on to the next prime number, which is 3.
- Continue dividing the number by prime numbers until you cannot divide it further.
- The remaining number is a prime number, and it is a factor of the original number.
Example: Prime Factorization of 12
Let’s find the prime factors of 12:
- Start by dividing 12 by 2: 12 ÷ 2 = 6
- Divide 6 by 2: 6 ÷ 2 = 3
- 3 is a prime number, so we cannot divide it further.
- Therefore, the prime factors of 12 are 2 × 2 × 3.
Exercise: Prime Factorization of 18
Find the prime factors of 18:
- Start by dividing 18 by 2: 18 ÷ 2 = 9
- 9 is not divisible by 2, so move on to the next prime number, which is 3.
- Divide 9 by 3: 9 ÷ 3 = 3
- 3 is a prime number, so we cannot divide it further.
- Therefore, the prime factors of 18 are 2 × 3 × 3.
More Exercises
Find the prime factors of the following numbers:
- 24: _______________________
- 30: _______________________
- 42: _______________________
- 48: _______________________
Table: Prime Factorization of Numbers 1-20
| Number | Prime Factors |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 2 × 2 |
| 5 | 5 |
| 6 | 2 × 3 |
| 7 | 7 |
| 8 | 2 × 2 × 2 |
| 9 | 3 × 3 |
| 10 | 2 × 5 |
| 11 | 11 |
| 12 | 2 × 2 × 3 |
| 13 | 13 |
| 14 | 2 × 7 |
| 15 | 3 × 5 |
| 16 | 2 × 2 × 2 × 2 |
| 17 | 17 |
| 18 | 2 × 3 × 3 |
| 19 | 19 |
| 20 | 2 × 2 × 5 |
💡 Note: Make sure to check your work by multiplying the prime factors together to ensure they equal the original number.
Conclusion
In this worksheet, we explored the concept of prime factorization and provided exercises for 6th-grade students to practice. By finding the prime factors of numbers, we can understand the building blocks of mathematics and develop essential skills in problem-solving and critical thinking. Remember to check your work by multiplying the prime factors together to ensure they equal the original number.
What is prime factorization?
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Prime factorization is the process of breaking down a composite number into a product of prime numbers.
What are prime numbers?
+
Prime numbers are positive integers that are divisible only by themselves and 1.
Why is prime factorization important?
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Prime factorization helps us understand the building blocks of mathematics and develops essential skills in problem-solving and critical thinking.
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