Class 6 · Maths · Ganita Prakash
Chapter 5 🔑
Chapter 5 🔑
Prime Time
Quick, colourful revision notes — easy to read before your test!
Chapter Contents
5.1 Multiples & Factors
Multiple of a number: what you get by multiplying it by 1, 2, 3, ... (e.g. multiples of 3: 3, 6, 9, 12, ...).
Factor (or divisor) of a number: a number that divides it exactly, with no remainder (e.g. factors of 24: 1, 2, 3, 4, 6, 8, 12, 24).
Factor (or divisor) of a number: a number that divides it exactly, with no remainder (e.g. factors of 24: 1, 2, 3, 4, 6, 8, 12, 24).
In the "idli-vada" game, players say "idli" for multiples of 3, "vada" for multiples of 5, and "idli-vada" for numbers that are multiples of both — these are common multiples (15, 30, 45, ...).
A jump size lands exactly on a number only if that jump size is a factor of the number. To land on two treasure numbers, the jump size must be a common factor of both.
5.2 Prime & Composite Numbers
Prime number — has exactly two factors: 1 and itself (e.g. 2, 3, 5, 7, 11...).
Composite number — has more than two factors (e.g. 4, 6, 8, 9...).
1 is neither prime nor composite — it has only one factor.
Composite number — has more than two factors (e.g. 4, 6, 8, 9...).
1 is neither prime nor composite — it has only one factor.
The Sieve of Eratosthenes is a neat way to find all primes up to a number — circle a prime, then cross out all its multiples, and repeat:
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Fig 1: All prime numbers from 1 to 50 (highlighted)
2 is the only even prime number — every other even number has 2 as an extra factor, so it can't be prime!
5.3 Co-prime Numbers
Two numbers are co-prime if they have no common factor other than 1 — even if neither of them is itself prime.
4 and 9 are co-prime (factors of 4: 1,2,4; factors of 9: 1,3,9 — only 1 is common).
15 and 39 are not co-prime — they share the common factor 3.
15 and 39 are not co-prime — they share the common factor 3.
5.4 Prime Factorisation
Prime factorisation — writing a number as a product of only prime numbers.
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Fig 2: Factor tree for 72 — keep splitting until every branch ends in a prime
Prime factorisation is a super-tool:
• Co-prime check — if two numbers share no common prime factor, they're co-prime.
• Divisibility check — a number is divisible by another only if the second's prime factorisation is fully "contained" in the first's.
• Co-prime check — if two numbers share no common prime factor, they're co-prime.
• Divisibility check — a number is divisible by another only if the second's prime factorisation is fully "contained" in the first's.
5.5 Divisibility Tests
Quick shortcuts to check factors — no long division needed!
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Fig 3: Divisibility rules for 2, 4, 5, 8 and 10
Is 8560 divisible by 8? Look only at the last 3 digits: 560 ÷ 8 = 70 exactly — so yes, 8560 is divisible by 8!
🎯 Quick Summary
- Multiple = product of a number with 1,2,3...; Factor = divides a number exactly.
- Prime = exactly 2 factors; Composite = more than 2 factors; 1 is neither.
- Sieve of Eratosthenes quickly finds all primes up to any number.
- Co-prime numbers share no common factor except 1.
- Prime factorisation writes any number as a product of primes — useful for checking co-primality and divisibility.
- Quick divisibility checks: 2→last digit even, 5→ends in 0/5, 10→ends in 0, 4→last 2 digits, 8→last 3 digits.
✏️ Notes by @edugrown — happy revising! 🍌