How to explain it
At this standard, students find the greatest common factor of two or three whole numbers using the listing-factors method and the prime-factorization method.
The anchor students hold onto: List all factors of each number and circle the largest one they share — OR write each number as a product of prime factors and multiply the primes that appear in every list. List the multiples of each number until you find the first one they share — OR write each number as a product of primes and multiply using the highest power of each prime.
GCF and LCM are companion skills in 6.NS.B.4. The LCM becomes the common denominator when adding unlike fractions in 6.NS.A.1 — both concepts appear together on that standard.
Worked examples
Example 1
Listing Factors
Find the GCF of 12 and 18.
Step 1Factors of 12: 1, 2, 3, 4, 6, 12
Step 2Factors of 18: 1, 2, 3, 6, 9, 18
Step 3Common factors: 1, 2, 3, 6
Step 4Greatest: GCF = 6
Answer6
Example 2
Prime Factorization
Find the GCF of 24 and 36.
Step 124 = 2 × 2 × 2 × 3
Step 236 = 2 × 2 × 3 × 3
Step 3Shared primes: 2 × 2 × 3
Step 4GCF = 12
Answer12
Example 3
Listing Multiples
Find the LCM of 4 and 6.
Step 1Multiples of 4: 4, 8, 12, 16..
Step 2Multiples of 6: 6, 12, 18..
Step 3First match: 12
Step 4LCM = 12
Answer12
Common mistakes
What students write
Stopped too early — GCF(12, 18) = 3 because that was the first common factor found.
The fix
List ALL common factors before choosing — 1, 2, 3, 6 are all common factors of 12 and 18, so GCF = 6.
What students write
Said GCF(6, 18) = 36 because "both 6 and 18 divide into 36."
The fix
A factor must DIVIDE INTO both numbers — it cannot be larger than either. 36 > 6, so 36 cannot be a factor of 6. GCF = 6.
What students write
Said LCM(4, 6) = 24 by just multiplying 4 × 6 — found a common multiple but not the LEAST one.
The fix
List multiples of each number to find the FIRST match — LCM(4, 6) = 12, which is less than 4 × 6 = 24.
What students write
Used lowest power instead of highest in prime factorization — LCM(4, 9): wrote 2¹ × 3¹ = 6 instead of 2² × 3² = 36.
The fix
Take each prime at its HIGHEST power across all numbers — 4 = 2², 9 = 3², so LCM = 2² × 3² = 4 × 9 = 36.
Teacher tip
Head off the two predictable errors before they happen. First: List ALL common factors before choosing — 1, 2, 3, 6 are all common factors of 12 and 18, so GCF = 6. Second: A factor must DIVIDE INTO both numbers — it cannot be larger than either. 36 > 6, so 36 cannot be a factor of 6. GCF = 6.