Factors and Multiples — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
The GCF of 12 and 18 is 3.
Corrected: The GCF of 12 and 18 is 6, because 6 is the largest number that divides both evenly.
The corrected sentence is: "The GCF of 12 and 18 is 6, because 6 is the largest number that divides both evenly." The error was wrong GCF value: the original sentence "The GCF of 12 and 18 is 3." needed to be fixed.
2. Fix the sentence:
Every even number is composite.
Corrected: Every even number greater than 2 is composite. The number 2 is even and prime.
The corrected sentence is: "Every even number greater than 2 is composite. The number 2 is even and prime." The error was forgot that 2 is prime: the original sentence "Every even number is composite." needed to be fixed.
3. Fix the sentence:
The LCM of 4 and 8 is 32.
Corrected: The LCM of 4 and 8 is 8, because 8 is already a multiple of 4.
The corrected sentence is: "The LCM of 4 and 8 is 8, because 8 is already a multiple of 4." The error was wrong LCM value: the original sentence "The LCM of 4 and 8 is 32." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The GCF of 20 and 30 is 10.
The factors of 20 are 1, 2, 4, 5, 10, 20 and the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. The largest they share is 10.
2. The LCM of 3 and 7 is 21.
Since 3 and 7 are both prime and share no common factors, their LCM is simply 3 × 7 = 21.
3. The factors of 32 are 1, 2, 4, 8, 16, and 32.
Every number is a factor of itself, so 32 completes the list: 1, 2, 4, 8, 16, 32.
4. The number 42 is divisible by 2, 3, 6, 7, and 14.
42 ÷ 14 = 3 with no remainder, so 14 is another factor of 42 along with 2, 3, 6, and 7.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. What is the difference between GCF and LCM? Give an example.
Sample answer: The GCF is the greatest factor two numbers share, while the LCM is the smallest multiple they share. For 6 and 8, the GCF is 2 and the LCM is 24.
A good answer includes: The GCF is the greatest factor two numbers share, while the LCM is the smallest multiple they share. For 6 and 8, the GCF is 2 and the LCM is 24.
2. Name all the prime numbers between 10 and 20.
Sample answer: The prime numbers between 10 and 20 are 11, 13, 17, and 19.
A good answer includes: The prime numbers between 10 and 20 are 11, 13, 17, and 19.