Prime Numbers and Prime Factorisation
A prime number is a whole number above 1 with exactly two factors: 1 and itself. So 7 is prime, but 6 is not because it also divides by 2 and 3. Prime factorisation writes a number as a product of primes, like 90 = 2 × 3² × 5.
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What is a Prime Number?
- A prime number has exactly two different factors: 1 and itself.
- 2 is the smallest prime number.
- 0 and 1 are not prime numbers.
Prime Numbers Below 20
- The prime numbers below 20 are: 2, 3, 5, 7, 11, 13, 17, 19.
- Remembering them helps you factorise larger numbers.
What Does Prime Factorisation Mean?
- Prime factorisation means writing a number as a product of prime numbers only.
- For example, .
Factor Tree Method for Prime Factorisation
- The factor tree method breaks a number into smaller factors step by step.
- Keep factorising until all factors are prime numbers.
Practice Questions
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Which of the following is a prime number?
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7 is a prime number because its only divisors are 1 and 7.
What is the smallest prime number?
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2 is the smallest prime number. It is the only even prime number because its only divisors are 1 and 2.
Which of the following numbers is NOT a prime number?
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15 is not a prime number because it is divisible by 3 and 5, making it a composite number.
Find the prime factorisation of 36.
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The prime factorisation of 36 is 2² × 3², as 36 can be broken down into the product of these prime factors: 2 × 2 × 3 × 3.
Find the prime factorisation of 144.
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The prime factorisation of 144 is 2⁴ × 3². This is because 144 can be broken down into 2 × 2 × 2 × 2 × 3 × 3.
Express 360 as a product of prime factors using indices.
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The correct prime factorisation of 360 is 2³ × 3² × 5. This is because 360 can be broken down into 2 × 2 × 2 × 3 × 3 × 5.
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Prime Numbers and Prime Factorisation frequently asked questions
The questions students bump into most on this topic
No, 1 is not a prime number. A prime number must have exactly two different factors, which are 1 and itself. The number 1 has only one factor, itself, so it does not meet this rule. This is why 2, not 1, is the smallest prime number.
Yes, 2 is a prime number because its only factors are 1 and 2. Having exactly two different factors is what makes a number prime. The number 2 is also the smallest prime number. That makes it an important starting point when you find prime factors.
Prime numbers are called the building blocks of maths because you can build every other number from them. Any natural number greater than 1 can be written as a product of prime numbers only. You multiply primes together, just as you build a wall from bricks.
The division method finds prime factors by dividing your number by prime numbers from smallest to largest. You start with 2, then move to the next prime each time the current one no longer divides exactly. You keep going until every factor left is a prime number.
We use indices to write repeated prime factors in a shorter, simpler way. For example, you can write 90 as 2 × 3 × 3 × 5. The repeated 3 becomes 3², which gives the neater form 2 × 3² × 5. This keeps long products quick to read.
Yes, prime factorisation is unique. Every natural number greater than 1 has only one set of prime factors. It does not matter which method you use to find them. The order you write the factors in can change. The primes, and how many times each appears, always stay the same.