How to Write 2,500 as a Product of Prime Factors Step by Step
FAQs on Prime Factorization of 2,500 for Class 6 Students
1. What are the prime factors of 2500?
The prime factors of 2,500 are 2, 2, 5, 5, 5, and 5. When these prime numbers are multiplied together, they equal 2,500. This is often written in exponential form for Class 6 Maths as 2² × 5⁴, which is the complete prime factorization of 2500.
2. How do you factor 2500 into primes step by step?
You can factor 2500 into primes step-by-step using the division method, a key technique in the Grade 6 syllabus. This method is straightforward and ensures you find all the prime factors correctly.
- Step 1: Start dividing 2500 by the smallest prime number, 2. You get 1250.
- Step 2: Divide 1250 by 2 again to get 625.
- Step 3: Since 625 is not divisible by 2 or 3, move to the next prime, 5. Divide 625 by 5 to get 125.
- Step 4: Continue dividing by 5 until you reach 1. (125 ÷ 5 = 25; 25 ÷ 5 = 5; 5 ÷ 5 = 1).
- Step 5: The prime factors are all the divisors you used: 2, 2, 5, 5, 5, 5.
3. What is the difference between factors and prime factors?
The key difference is that factors can be any number that divides another number without a remainder, while prime factors must strictly be prime numbers. This is a fundamental concept in the Number System for Class 6.
- Factors of 12: 1, 2, 3, 4, 6, 12. This list includes both prime (2, 3) and composite (4, 6, 12) numbers.
- Prime Factors of 12: 2, 2, 3. This list includes only the prime numbers that multiply to make 12.
4. Can factor trees help find prime factors?
Yes, factor trees are a highly effective visual tool for finding prime factors, often taught in Class 6. This method helps in breaking down a number into its prime components systematically.
You start with the number (e.g., 2500) and split it into two factors (like 25 and 100). You continue to split any composite numbers into smaller factors until all the 'branches' end in a prime number. This worksheet includes factor tree activities to help students master this method.
5. What is the prime factorization of 2500 using the division method?
The prime factorization of 2500 using the division method is 2 × 2 × 5 × 5 × 5 × 5. This is found by continuously dividing 2500 by the smallest possible prime numbers until the quotient is 1.
- 2500 ÷ 2 = 1250
- 1250 ÷ 2 = 625
- 625 ÷ 5 = 125
- 125 ÷ 5 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
This method reinforces division skills and helps in understanding factors and multiples.
6. How can I use this worksheet at home?
This Class 6 Maths worksheet is perfect for use at home to support learning and practice. It is designed to be student-friendly and requires minimal parental supervision.
- Homework Help: Use it as a resource for completing school assignments on prime factorization.
- Revision: It serves as an excellent tool for revising the topic of factors and multiples before exams.
- Concept Reinforcement: The fill-in-the-blank exercises and practice problems help strengthen understanding beyond rote learning.
7. Does this worksheet include an answer key?
Yes, a detailed answer key is included with this prime factorization worksheet. This feature is crucial for effective self-study and allows parents to easily check their child's work.
The answer key provides stepwise solutions, helping students understand the correct process for both the division method and factor trees, ensuring they can learn from their mistakes.
8. Is this worksheet printable?
Absolutely. This worksheet is available as a free, printable PDF designed for easy home or classroom use. The layout is optimized with age-appropriate fonts and sufficient space for students to write their solutions, making it a convenient resource for parents and teachers following the NCERT syllabus.
9. What skills are built by this activity?
This activity builds several crucial mathematical skills that are foundational for higher-grade maths. It goes beyond simple calculation and encourages deeper numerical understanding.
- Number System Fluency: Deepens understanding of prime vs. composite numbers.
- Logical Reasoning: Promotes systematic thinking to break down complex numbers.
- Multiplication and Division: Provides practical application and practice of core arithmetic skills.
- Critical Thinking: Helps students develop strategies for factoring both small and large numbers efficiently.
10. Can I use this worksheet digitally on a tablet?
Yes, this worksheet is provided in a PDF format that is fully compatible with tablets and other digital devices. Students can download the file and use it with any PDF reader or note-taking app that supports a stylus, allowing them to complete the exercises without needing a printer.
