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§ Arithmetic·Grade 6

Factors, GCF & LCM Worksheets

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Easy

10 problems

Medium

20 problems

Hard

20 problems

Mixed

30 problems

Free printable factors, gcf & lcm worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from gcf by listing factors at the easy level through to gcf or lcm, large numbers at the advanced level.

CCSS.6.NS

What is factors, gcf & lcm?

Factors are whole numbers that divide evenly into another number without leaving a remainder. The Greatest Common Factor (GCF) represents the largest number that divides into two or more numbers, while the Least Common Multiple (LCM) is the smallest number that both original numbers divide into evenly. These concepts appear in CCSS Grade 4 standards for finding factor pairs and identifying prime and composite numbers.

Why it matters

Factors, GCF, and LCM solve practical problems across multiple domains. In construction, finding the GCF of measurements like 24 inches and 36 inches (GCF = 12) helps determine the largest tile size that fits evenly. Scheduling problems use LCM — if one bus arrives every 15 minutes and another every 20 minutes, they meet every 60 minutes (LCM of 15 and 20). These concepts underpin fraction operations, since adding 112 + 118 requires finding LCM(12,18) = 36 for the common denominator. In algebra, factoring polynomials builds directly on number factoring skills. Manufacturing uses GCF to determine efficient packaging sizes, while computer science applies these concepts in algorithm optimization and data structure design.

Common mistakes to watch for

  • ✗Confusing GCF and LCM leads to writing GCF(8,12) = 24 instead of 4, mixing up the greatest common factor with the least common multiple.
  • ✗Missing factors when listing creates incomplete factor sets, such as listing factors of 12 as {1,2,3,6,12} while omitting 4.
  • ✗Using the LCM formula incorrectly results in calculating LCM = (a × b) × GCF instead of LCM = (a × b) ÷ GCF, producing 12 × 18 × 6 = 1296 rather than 36.

Questions teachers ask

What is the difference between GCF and LCM?+
GCF finds the largest number that divides into both original numbers, while LCM finds the smallest number that both original numbers divide into. For 6 and 8, GCF = 2 (largest common divisor) and LCM = 24 (smallest common multiple).
How do you find the GCF of three numbers?+
List factors of all three numbers and identify the largest factor common to all lists. For GCF(12, 18, 24): factors are {1,2,3,4,6,12}, {1,2,3,6,9,18}, and {1,2,3,4,6,8,12,24}. The common factors are {1,2,3,6}, so GCF = 6.
Can the GCF be larger than one of the original numbers?+
No, the GCF cannot exceed the smallest of the original numbers. Since factors must divide evenly into a number, no factor can be larger than the number itself. The maximum possible GCF equals the smaller number when one divides the other.
What happens when two numbers have no common factors except 1?+
Numbers with GCF = 1 are called relatively prime or coprime. Examples include 15 and 28, where GCF(15,28) = 1. Their LCM equals their product: LCM(15,28) = 15 × 28 = 420, since they share no common factors to reduce the calculation.
How do you check if your GCF answer is correct?+
Divide both original numbers by the proposed GCF. Both results must be whole numbers with no common factors except 1. For GCF(20,30) = 10: check 20÷10 = 2 and 30÷10 = 3. Since GCF(2,3) = 1, the answer is correct.
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Beginner

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Concepts
GCF by listing factors
Range
4–12
Steps
3 steps
Example
GCF of 8 and 12

Easy

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Concepts
GCF or LCM, small numbers
Range
6–30
Steps
3 steps
Example
LCM of 6 and 10

Medium

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Concepts
GCF or LCM, medium numbers
Range
6–60
Steps
3 steps
Example
GCF of 24 and 36

Hard

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Concepts
GCF or LCM, large numbers
Range
20–100
Steps
3 steps
Example
LCM of 45 and 60

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