Prime, Composite & Divisibility Rules explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
Revise the definition, formulae, important results, and exam method first.
Use the sticky diagram while this dedicated tool is being prepared.
Solve only this concept and let the app adapt from your answers.
You have met the idea. Now open a tiny puzzle, a useful fact, and the next best action.
Continue the journey
Prime and composite numbers help us understand how numbers are built.
Divisibility rules help us decide quickly whether one number divides another exactly.
These ideas are needed for simplifying fractions, finding HCF and LCM, and solving many number problems.
A factor divides a number exactly. For example, 4 is a factor of 20 because with no remainder.
A prime number has exactly two factors: 1 and itself. A composite number has more than two factors.
The number 1 is neither prime nor composite. It has only one factor.
Prime factorisation breaks a number into prime factors. The final prime factors multiply back to the original number.
Meaning: Factors divide a number exactly. Multiples are results of multiplying a number.
Definition: If a x , then a and b are factors of c, and c is a multiple of a and b.
For 24, factors include 1, 2, 3, 4, 6, 8, 12, and 24. Multiples of 6 include 6, 12, 18, 24, and so on.
Meaning: Prime numbers cannot be split into smaller wholumber factors except 1 and itself.
Definition: A prime number is greater than 1 and has exactly two factors.
2, 3, 5, 7, 11, and 13 are prime. 4, 6, 8, 9, and 10 are composite.
Meaning: Divisibility rules are quick tests for exact division.
Definition: A number is divisible by another number if division leaves no remainder.
For example, a number is divisible by 3 if the sum of its digits is divisible by 3.
Meaning: Prime factorisation writes a number as a product of primes.
Definition: It is the complete breakdown of a number into prime factors.
For 84, divide by primes: x x 2 x x 2 x 3 x 7.
Easy
Question: Is 31 prime?
Medium
Question: Use divisibility rules to check if 738 is divisible by 2, 3, and 9.
Exam-level
Question: Prime factorise 180.
Calling 1 a prime number
Why it happens: Students remember that prime numbers divide by 1.
Correct approach: Prime numbers must have exactly two factors. 1 has only one factor.
Stopping before all factors are prime
Why it happens: A factor tree may contain numbers like 6 or 15.
Correct approach: Keep splitting until every branch ends in a prime.
Testing too many numbers for primality
Why it happens: Students do not know where to stop.
Correct approach: Test prime divisors up to the square root of the number.
Why is 2 prime?
It has exactly two factors: 1 and 2.
Can an even number be prime?
Only 2. Every other even number has 2 as an extra factor.
Why learn prime factorisation?
It is a reliable method for HCF, LCM, and simplifying fractions.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.