Prime Factorization Worksheets

There are six sets of factors & multiples worksheets:

• Factors
  
• Prime Factorization
  
• Greatest Common Factor
  
• Multiples
  
• Least Common Multiple
  
• LCM and GCF
  

Examples, solutions, videos, and worksheets to help Grade 4 students learn how to find the prime factorization of a number.

How to find the prime factorization of a number?

There are two sets of prime factorization worksheets.

• Prime Factorization (Numbers < 50).
• Prime Factorization (Write as exponents).

Prime factorization is the process of expressing a composite number as a product of its prime factors. A prime factor is a prime number that can divide the original number evenly. Here’s how to find the prime factorization of a number:

1. Find the Smallest Prime Factor
   Start by dividing the number by the smallest prime number, which is 2. If 2 divides evenly, it’s a factor. Keep dividing by 2 until it no longer divides evenly. Write down each 2 as a factor.
2. Move to the Next Prime
   After you’ve divided by 2 as many times as possible, move to the next prime number, which is 3. Repeat the process, dividing by 3 until it no longer divides evenly. Write down each 3 as a factor.
3. Continue with Larger Primes
   Continue this process, moving to larger prime numbers like 5, 7, 11, and so on, until you’ve completely factored the number into prime factors. You don’t need to check prime numbers larger than the square root of the remaining part of the number.
4. Write the Prime Factorization
   Write the prime factorization as a product of the prime factors you found.

For example, find the prime factorization of 72:
72 is even, so divide by 2:
72÷2=36. Write down 2 as a factor.
36 is also even, so divide by 2 again:
36÷2=18. Write down another 2 as a factor.
Continue with 18. 18 is divisible by 2:
18÷2=9. Write down another 2 as a factor.
Now, 9 is not divisible by 2. Try the next prime, which is 3.
9÷3=3. Write down 3 as a factor.
Finally, you’re left with 3, which is already a prime number.
Now, write down all the prime factors together:
2 x 2 x 2 x 3 x 3 = 72

Have a look at this video if you need to review the Prime Factorization.

• Prime Factorization

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Prime Factorization Worksheets.

 

More Prime Factorization Worksheets

Printable
(Answers on the second page.)
Prime Factorization Worksheet #1 (Numbers < 50)
Prime Factorization Worksheet #2 (Write as exponents)

Online
Prime & Composite Numbers up to 10
Prime & Composite Numbers up to 20

Find Missing Factor
Greatest Common Factor
GCF or HCF

GCF and LCM Word Problems

Related Lessons & Worksheets

Factors & Multiples

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