Common Factors
About This Worksheet
This worksheet helps sixth-grade students find the greatest common factor of two whole numbers. Students first list the factors of each number, circle the factors the pair shares, and then identify the greatest common factor. This step-by-step format makes the process easy to follow because students can see exactly how the two factor lists overlap. The activity emphasizes understanding what “common” and “greatest” mean instead of jumping directly to an answer. It is a strong bridge from basic factor work into more formal GCF problem solving.
What Students Practice
Students create complete factor lists for number pairs such as 8 and 12, 15 and 25, 18 and 30, and larger combinations. They compare the lists, locate factors that appear in both, and determine which shared factor has the greatest value. This gives them repeated practice with factor fluency and careful comparison. The larger number pairs also require students to organize their lists so they do not miss any factors. By writing the GCF after identifying the common factors, students connect the full reasoning process to the final result.
Why This Matters
The greatest common factor is useful whenever students need to divide quantities into the largest equal groups or simplify numerical relationships. Understanding the factor-list method also helps students see what GCF actually means before they move to faster strategies such as prime factorization. This skill supports fraction simplification, distributive-property work, and many real-world grouping problems. Students who understand why a factor is common are less likely to confuse GCF with LCM. That distinction becomes increasingly important as number theory problems become more complex.
Teaching Tips
Have students list factors in numerical order so matching common factors is easier to see. Encourage them to check each list by pairing factors from the outside inward, such as 1 with the number itself. Once the common factors are circled, ask students why the largest shared value is the GCF. If they miss a factor, use division or multiplication facts to check whether another factor pair exists. You can also challenge students to predict the GCF before completing the full lists and then verify their prediction.
Curriculum Standards
This worksheet directly supports CCSS.MATH.CONTENT.6.NS.B.4, which asks sixth-grade students to find the greatest common factor of two whole numbers less than or equal to 100. The factor-list approach gives students a concrete method for meeting that standard. It also reinforces factor fluency and prepares students for using the distributive property with common factors. The activity is appropriate for guided practice, independent work, homework, or intervention during a Grade 6 number theory unit.