Common Factors
4A · Chapter 3 · Lesson 5 · MATH-4A-C03-L05
Learning goal. Find common factors and the greatest common factor, connecting them to equal grouping.
Before you begin
Recall: Grade 3: arrays and multiplication tables; 4A Ch2: addition strategies; Prime Numbers and Composite Numbers. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Classify 57 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 3, 19, 57. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 54 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 2, 3, 6, 9, 18, 27, 54. Prime means exactly two positive factors; 1 is neither prime nor composite.
Classify 67 as prime, composite, or neither.
Show answer & reasoning
The positive factors are 1, 67. Prime means exactly two positive factors; 1 is neither prime nor composite.
Key vocabulary
- multiple
- whole-number product of a given number
- factor
- whole number dividing exactly
- prime
- positive number with exactly two positive factors
- composite
- positive number with more than two positive factors
Understand the concept
A common factor divides two quantities exactly. To find the greatest common factor, list factor pairs and identify the largest number in both lists. If you have 18 red and 24 blue counters and want equal groups of each color with none left over, six groups is the largest possible number of groups.
Model it: factor intersection and grouping model. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
What is the greatest common factor of 18 and 12?
The GCF is the largest whole number dividing both with no remainder: 6.
Check your understanding 1
What is the greatest common factor of 18 and 45?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 9.
Worked example 2
What is the greatest common factor of 24 and 33?
The GCF is the largest whole number dividing both with no remainder: 3.
Check your understanding 2
What is the greatest common factor of 14 and 30?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 2.
Worked example 3
What is the greatest common factor of 12 and 15?
The GCF is the largest whole number dividing both with no remainder: 3.
Check your understanding 3
What is the greatest common factor of 26 and 33?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 1.
Guided practice
What is the greatest common factor of 8 and 36?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 4.
What is the greatest common factor of 12 and 39?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 3.
What is the greatest common factor of 18 and 33?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 3.
What is the greatest common factor of 6 and 15?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 3.
What is the greatest common factor of 8 and 39?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 1.
Independent practice
What is the greatest common factor of 14 and 21?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 7.
What is the greatest common factor of 12 and 33?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 3.
What is the greatest common factor of 32 and 39?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 1.
What is the greatest common factor of 14 and 24?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 2.
What is the greatest common factor of 16 and 27?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 1.
What is the greatest common factor of 14 and 45?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 1.
What is the greatest common factor of 26 and 18?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 2.
What is the greatest common factor of 32 and 30?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 2.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A learner says the greatest common factor of 12 and 18 is 36 because both multiply into 36. Find the GCF.
Show answer & reasoning
A common factor divides both numbers; 6 is the largest positive divisor shared by 12 and 18.
What is the greatest common factor of 24 and 12?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 12.
Exit check
What is the greatest common factor of 12 and 45?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 3.
What is the greatest common factor of 16 and 21?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 1.
What is the greatest common factor of 30 and 27?
Show answer & reasoning
The GCF is the largest whole number dividing both with no remainder: 3.