Prime Numbers
Class 6 Maths · Chapter 5: Prime Time · NCERT Ganita Prakash section 5.2
Learn
Rohan has 12 square tiles. He can make many rectangles: 1 × 12, 2 × 6 and 3 × 4. But with 7 tiles, the only rectangle is a single line, 1 × 7.
A number with exactly two factors, 1 and itself, is a prime number: 2, 3, 5, 7, 11, 13 … A number with more than two factors is composite: 4, 6, 8, 9, 10 … The number 1 has only one factor, so it is neither prime nor composite.
Finding primes with a sieve: write the numbers. Circle 2 and cross out every other multiple of 2. Circle 3 and cross out its multiples. Do the same for 5 and 7. The numbers left (except 1) are all the primes up to 100. This idea is over 2,000 years old!
Only one even number is prime: 2. Every other even number divides by 2, so it has at least three factors.
Explore: build rectangles, then hunt for primes.
- Make a rectangle with 12 squares (not a single line).
- Now try 7 squares. Can you make anything except a single line?
- Tap every prime number from 1 to 30.
Remember
- Prime: exactly two factors (1 and itself). Composite: more than two. 1 is neither.
- 2 is the only even prime. The sieve finds primes by crossing out multiples.
Quick check
Which of these numbers is prime?
- 21
- 27
- 29
- 33
Answer
29. 29 divides only by 1 and 29. 21 = 3 × 7, 27 = 3 × 9 and 33 = 3 × 11.
Think about it
Kabir says: 'Every odd number is prime.' Is he right?
One answer
No. 9 = 3 × 3, 15 = 3 × 5 and 21 = 3 × 7 are odd but composite. (Also, 2 is prime and it is even.)
Practice
Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.