What are Prime Numbers?
Prime numbers are whole numbers greater than 1 that are not a product of two other whole numbers. For example, 2 is a prime number because it can only be a product of 1 and itself 12; no other two numbers can be multiplied to make 2. The numbers 3, 5, and 7 are also prime numbers. Remember that prime numbers are whole, positive numbers – they can’t be fractions and decimals.
If a whole number can be formed by multiplying two numbers other than itself, then it’s a composite number. The number 10 is a composite because it’s a product of other numbers: 25. We can say that 2 and 5 are factors of 10. Factors are numbers that we multiply to get a product.
Here’s a chart of prime and composite numbers from 2-50. Take note that 1 is neither a prime nor a composite number. The prime numbers are highlighted in blue.
Prime Factorization: How to Find the Prime Factors of a Composite Number
Prime factorization refers to the method of finding the prime numbers that are factors of a given number. It means breaking the given number down to its last prime factor.
Example #1: Find the Prime Factors of 44 Using Prime Factorization
Solution to Example #1:
Step 1. Divide the composite number, 44, by a prime number, such as 2.
44 / 2 = 22
Step 2. Since 22 is still a composite number, break it down further. Divide it by 2 again.
22 / 2 = 11
Step 3. Now we’ve reached the last prime factor! This gives us the answer:
44 = 2 • 2 • 11
Therefore, the prime factors of 44 are 2 • 2 • 11 or 22 • 11.
Example #2: Find the Prime Factors of 154 Using Prime Factorization
Solution to Example #2:
Step 1. We’re working with a bigger composite number in this example, so let’s divide by a bigger prime number.
Remember that we don’t work on decimals in factorization. Let’s try using the prime number 11.
154 / 11 = 14
Step 2. Divide 14 by another prime number, 7.
14 / 7 = 2
Therefore, the prime factors of 154 are 2 • 7 • 11.
Factor Tree
Another way of factorizing a number is through the factor tree – a visual way of diagramming the factors of a number. To create the diagram, start with the two factors of a given number, then extract the factors of those first two numbers until you reach the last prime factor. As the name suggests, the resulting diagram looks like a tree.
Example #3: Find the Prime Factors of 92 Using a Factor Tree
Solution to Example #3:
Start by finding the first two factors of 92.
We know that 46 • 2 = 92 so write them below 92.
Then factor 46 into 23 • 2.
Since 23 and 2 are prime numbers, we can’t extract them further.
Therefore, the prime factors of 92 are 2 • 2 • 23 or 22 • 23.
Example #4: Find the Prime Factors of 45 Using a Factor Tree
Solution to Example #4:
We know that 15 • 3 = 45 so write them below 45.
Then factor 15 into 3 • 5.
3 and 5 are both prime numbers.
Therefore, the prime factors of 45 are 3 • 3 • 5 or 32 • 5.
Example #5: Find the Prime Factors of 126 Using a Factor Tree
Solution to Example #5:
Divide 126 by a relatively big prime number, 7, to come up with its factors:
126 / 7 = 18
Write 18 and 7 as factors below 126.
Then factor 18 into 9 • 2.
Factor 9 again into 3 • 3.
Therefore, the prime factors of 126 are 2 • 3 • 3 • 7 or 2 • 32 • 7.
Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the prime numbers and prime factorization.
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