Prime Time — Class 6 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Prime Time" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Prime Time" — 8 important questions with detailed answers for CBSE board exam prepa…
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Key Questions Covered:
- What is the difference between a prime number and a composite number?
- List all prime numbers between 10 and 30.
- Find all factors of 36.
- Write the first five multiples of 7.
- Find the HCF of 12 and 18 using the listing method.
- Is 1 a prime number? Explain why or why not.
- + 2 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| What is the difference between a prime number and a compo… | ✓ Solved |
| List all prime numbers between 10 and 30. | ✓ Solved |
| Find all factors of 36. | ✓ Solved |
| Write the first five multiples of 7. | ✓ Solved |
| Find the HCF of 12 and 18 using the listing method. | ✓ Solved |
| Is 1 a prime number? Explain why or why not. | ✓ Solved |
Showing 6 of 8 questions
Q1: What is the difference between a prime number and a composite number?
Step 1: Define a prime number
A prime number is a number greater than 1 that has exactly two factors: 1 and itself
Example: 7 is prime because only 1 and 7 divide it evenly
Factors of 7: 1, 7
Step 2: Define a composite number
A composite number is a number greater than 1 that has more than two factors
Example: 8 is composite because 1, 2, 4, and 8 all divide it evenly
Factors of 8: 1, 2, 4, 8
Step 3: Note about 1
1 is neither prime nor composite (it has only one factor: itself)
Step 4: Compare
P...
Q2: List all prime numbers between 10 and 30.
A prime number has exactly two factors: 1 and itself.
Step 1: Check each number from 10 to 30
10: factors are 1, 2, 5, 10 → composite (more than 2 factors)
11: factors are 1, 11 → prime ✓
12: factors are 1, 2, 3, 4, 6, 12 → composite
13: factors are 1, 13 → prime ✓
14: factors are 1, 2, 7, 14 → composite
15: factors are 1, 3, 5, 15 → composite
16: factors are 1, 2, 4, 8, 16 → composite
17: factors are 1, 17 → prime ✓
18: factors are 1, 2, 3, 6, 9, 18 → composite
19: factors are 1, 19 → prime ✓
2...
Q3: Find all factors of 36.
Factors are numbers that divide evenly into another number (with no remainder).
Step 1: Test each number starting from 1
36 ÷ 1 = 36 → 1 and 36 are factors
36 ÷ 2 = 18 → 2 and 18 are factors
36 ÷ 3 = 12 → 3 and 12 are factors
36 ÷ 4 = 9 → 4 and 9 are factors
36 ÷ 5 = 7.2 → 5 is not a factor
36 ÷ 6 = 6 → 6 is a factor
Step 2: Continue up to the square root
We only need to check up to √36 = 6
Step 3: List all factors in order
Step 4: Organize
1, 2, 3, 4, 6, 9, 12, 18, 36
Answer: The factors of 36 ...
Q4: Write the first five multiples of 7.
Multiples are numbers you get when you multiply a number by 1, 2, 3, 4, ...
Step 1: Multiply 7 by 1
7 × 1 = 7 (1st multiple)
Step 2: Multiply 7 by 2
7 × 2 = 14 (2nd multiple)
Step 3: Multiply 7 by 3
7 × 3 = 21 (3rd multiple)
Step 4: Multiply 7 by 4
7 × 4 = 28 (4th multiple)
Step 5: Multiply 7 by 5
7 × 5 = 35 (5th multiple)
Answer: The first five multiples of 7 are: 7, 14, 21, 28, 35
Q5: Find the HCF of 12 and 18 using the listing method.
The HCF (Highest Common Factor) is the largest number that divides both numbers.
Step 1: List all factors of 12
Factors of 12: 1, 2, 3, 4, 6, 12
Step 2: List all factors of 18
Factors of 18: 1, 2, 3, 6, 9, 18
Step 3: Identify common factors (factors in both lists)
Common factors: 1, 2, 3, 6
Step 4: Find the highest common factor
HCF = 6
Step 5: Verify
12 ÷ 6 = 2 ✓
18 ÷ 6 = 3 ✓
Answer: The HCF of 12 and 18 is 6
Q6: Is 1 a prime number? Explain why or why not.
Step 1: Recall the definition of a prime number
A prime number is a natural number greater than 1 that has exactly two distinct factors: 1 and itself
Step 2: Check the factors of 1
The only factor of 1 is 1 itself
1 has only 1 factor (itself), not 2 factors
Step 3: Apply the definition
Since 1 has only one factor (not two), it does not fit the definition of a prime number
Step 4: Also note
1 also does not fit the definition of a composite number (which needs more than 2 factors)
So 1 is in a spe...
Showing 6 of 8 questions. Visit the full page for complete solutions.
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