Schooling · Class 6 · Mathematics · Prime Time · Chapter on a page
CBSE Class 6 · Mathematics · NCERT Ganita Prakash
Prime Time: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- factor
- A prime number has exactly two factors
- composite number
- The number 1 is special. It has only…
- 2 is the smallest prime and the only…
- Prime factorisation
- Every composite number can be…
- Formulas and facts
- Finding factors
- Prime check rule
- Prime factorisation by division
- Useful small primes
- Divisibility shortcut for 2
- Divisibility shortcut for 3
- Watch out for
- Thinking 1 is a prime number
- Forgetting that 2 is prime because…
- Stopping prime factorisation too…
- Confusing factors and multiples
- Missing factor pairs (e.g., listing…
What this chapter is about
This chapter is about special whole numbers called prime numbers and their cousins, composite numbers. You will learn how to tell if a number is prime or composite by looking at its factors.
Key ideas
- A factor of a number divides it exactly with no remainder. For example, factors of 12 are 1, 2, 3, 4, 6 and 12.
- A prime number has exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
- A composite number has more than two factors. Examples: 4, 6, 8, 9, 10, 12.
- The number 1 is special. It has only one factor (itself), so it is neither prime nor composite.
- 2 is the smallest prime and the only even prime number. Every other even number is composite.
- Prime factorisation means writing a number as a product of primes. For example, 18 = 2 × 3 × 3.
- Every composite number can be written as a product of primes in only one way (ignoring order). This is called the Fundamental Theorem of Arithmetic.
- To test if a small number is prime, check whether any prime less than it divides it exactly.
Formulas and facts to remember
- Finding factors: Divide the number by 1, 2, 3, … and list all divisors that give remainder 0.
- Prime check rule: If no number from 2 up to just below the number divides it, the number is prime.
- Prime factorisation by division: Keep dividing by the smallest prime that works until you reach 1. Collect all the primes used.
- Useful small primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
- Divisibility shortcut for 2: A number ending in 0, 2, 4, 6 or 8 is divisible by 2.
- Divisibility shortcut for 3: If the sum of digits is divisible by 3, the number is divisible by 3.
Common mistakes
- Thinking 1 is a prime number → Remember, 1 has only one factor, so it is neither prime nor composite.
- Forgetting that 2 is prime because it is even → 2 is the only even prime; all other even numbers are composite.
- Stopping prime factorisation too early (e.g., writing 12 = 3 × 4) → Keep going: 4 = 2 × 2, so 12 = 2 × 2 × 3.
- Confusing factors and multiples → Factors divide the number; multiples are the number times 1, 2, 3, …
- Missing factor pairs (e.g., listing only small factors) → Check pairs: if 2 divides 28, then 28 ÷ 2 = 14 is also a factor.
Quick revision
- A prime has exactly two factors: 1 and itself.
- A composite has more than two factors.
- 1 is neither prime nor composite.
- 2 is the smallest and only even prime.
- Prime factorisation breaks a number into a product of primes.
- Always divide by the smallest prime first when factorising.