Prime Numbers
A prime number has exactly two factors: 1 and itself. Every whole number greater than 1 can be written as a product of primes.
The first few prime numbers are Notice that 2 is the only even prime. Every other even number can be divided by 2, so it has more than two factors.
Any whole number greater than 1 that is not prime is called composite. You can break a composite number down into prime factors using a factor tree. Pick any factor pair, split the number, and keep going until every branch ends at a prime.
The diagram below builds a factor tree for you. Try entering 60 to see how .
Watch it work
Question: Write 180 as a product of its prime factors.
Step 1: 180 is even, so divide by 2. .
Step 2: 90 is even, so divide by 2 again. .
Step 3: 45 is odd. Try 3: .
Step 4: . Both 3 and 5 are prime, so we stop.
Answer: .
Have a go
Q1. Is 51 a prime number? Explain.
Check divisibility: . Since 3 divides 51 exactly, 51 has more than two factors.
No. , so it is not prime.
Q2. Write 72 as a product of its prime factors.
, , , .
Q3. Write 100 as a product of its prime factors.
, , .
Q4. List all the prime numbers between 30 and 50.
Check each odd number (even numbers other than 2 are not prime):
31: not divisible by 2, 3, or 5. Prime.
33: . Not prime.
35: . Not prime.
37: not divisible by 2, 3, or 5. Prime.
39: . Not prime.
41: prime. 43: prime. 45: not prime. 47: prime. 49: , not prime.