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 20 are 1, 2, 5, 10, and 20.
Corrected: The factors of 20 are 1, 2, 4, 5, 10, and 20.
The corrected sentence is: "The factors of 20 are 1, 2, 4, 5, 10, and 20." The error was missing factor: the original sentence "The factors of 20 are 1, 2, 5, 10, and 20." needed to be fixed.
2. Fix the sentence:
A number is divisible by 3 if it ends in 3.
Corrected: A number is divisible by 3 if the sum of its digits is divisible by 3.
The corrected sentence is: "A number is divisible by 3 if the sum of its digits is divisible by 3." The error was wrong divisibility rule: the original sentence "A number is divisible by 3 if it ends in 3." needed to be fixed.
3. Fix the sentence:
The first four multiples of 9 are 9, 18, 36, 45.
Corrected: The first four multiples of 9 are 9, 18, 27, 36.
The corrected sentence is: "The first four multiples of 9 are 9, 18, 27, 36." The error was skipped a multiple: the original sentence "The first four multiples of 9 are 9, 18, 36, 45." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The number 30 is divisible by 2, 3, 5, and 10.
30 ÷ 10 = 3 with no remainder, so 10 is another factor of 30 along with 2, 3, and 5.
2. The factors of 16 are 1, 2, 4, 8, and 16.
Every number is a factor of itself, so 16 is the last factor in the list: 1, 2, 4, 8, 16.
3. A number with exactly two factors is called a prime number.
A prime number has only 1 and itself as factors -- exactly two factors total, like 2, 3, 5, or 7.
4. The sixth multiple of 5 is 30.
Multiply 5 × 6 = 30. The multiples of 5 in order are 5, 10, 15, 20, 25, 30, so the sixth one is 30.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Is 49 prime or composite? Explain how you know.
Sample answer: 49 is composite because 7 × 7 = 49, so it has factors other than 1 and itself.
A good answer includes: 49 is composite because 7 × 7 = 49, so it has factors other than 1 and itself.
2. List all the factor pairs of 36.
Sample answer: The factor pairs of 36 are 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 and 6.
A good answer includes: The factor pairs of 36 are 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 and 6.