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 factors of 12 are 1, 2, 3, 6, and 12.
Corrected: The factors of 12 are 1, 2, 3, 4, 6, and 12.
The corrected sentence is: "The factors of 12 are 1, 2, 3, 4, 6, and 12.". The original sentence "The factors of 12 are 1, 2, 3, 6, and 12." contained an error that needed to be fixed.
2. Fix the sentence:
15 is a prime number because it ends in 5.
Corrected: 15 is a composite number because it has factors other than 1 and itself, such as 3 and 5.
The corrected sentence is: "15 is a composite number because it has factors other than 1 and itself, such as 3 and 5.". The original sentence "15 is a prime number because it ends in 5." contained an error that needed to be fixed.
3. Fix the sentence:
The first five multiples of 4 are 4, 8, 12, 16, 24.
Corrected: The first five multiples of 4 are 4, 8, 12, 16, 20.
The corrected sentence is: "The first five multiples of 4 are 4, 8, 12, 16, 20.". The original sentence "The first five multiples of 4 are 4, 8, 12, 16, 24." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A factor of a number divides it with no remainder.
By definition, a factor divides a number evenly — no remainder left over.
2. The number 1 is a factor of every number.
1 divides every whole number evenly, so it is a factor of all whole numbers.
3. The first three multiples of 6 are 6, 12, and 18.
6 × 1 = 6, 6 × 2 = 12, 6 × 3 = 18.
4. A number that has exactly two factors is called prime.
A prime number has exactly two factors: 1 and itself.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. What is the difference between a factor and a multiple?
Sample answer: A factor divides evenly into a number, while a multiple is the result of multiplying that number by a whole number. For example, 3 is a factor of 12 and 12 is a multiple of 3.
Students should contrast division (factors) with multiplication (multiples) and ideally give a numerical example.
2. List all the factor pairs of 24.
Sample answer: The factor pairs of 24 are 1 and 24, 2 and 12, 3 and 8, and 4 and 6.
24 = 1×24, 2×12, 3×8, 4×6 — four factor pairs total.