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:
2 is composite because it is even.
Corrected: 2 is prime because its only factors are 1 and 2. It is the only even prime number.
The corrected sentence is: "2 is prime because its only factors are 1 and 2. It is the only even prime number.". The original sentence "2 is composite because it is even." contained an error that needed to be fixed.
2. Fix the sentence:
9 is prime because it is odd.
Corrected: 9 is composite because 3 × 3 = 9, so it has factors other than 1 and itself.
The corrected sentence is: "9 is composite because 3 × 3 = 9, so it has factors other than 1 and itself.". The original sentence "9 is prime because it is odd." contained an error that needed to be fixed.
3. Fix the sentence:
1 is a prime number because its only factor is itself.
Corrected: 1 is neither prime nor composite because a prime number must have exactly two distinct factors.
The corrected sentence is: "1 is neither prime nor composite because a prime number must have exactly two distinct factors.". The original sentence "1 is a prime number because its only factor is itself." 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 composite number has more than 2 factors.
Composite numbers have more than 2 factors (1 and itself), meaning they have at least one other factor.
2. A number is divisible by 2 if its last digit is even.
Divisibility rule for 2: the last digit must be 0, 2, 4, 6, or 8 (an even digit).
3. A number is divisible by 5 if it ends in 0 or 5.
Divisibility rule for 5: the last digit must be 0 or 5.
4. The smallest prime number is 2.
2 is the smallest prime number and the only even prime number.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain how you can quickly tell if 45 is divisible by 3.
Sample answer: Add the digits: 4 + 5 = 9. Since 9 is divisible by 3, the number 45 is also divisible by 3.
The divisibility rule for 3: add all digits; if the sum is divisible by 3, the number is too.
2. Is 37 prime or composite? How do you know?
Sample answer: 37 is prime because no number other than 1 and 37 divides it evenly. It is not divisible by 2, 3, 4, 5, or 6.
To check if 37 is prime, test divisibility by all primes up to its square root (≈6.1): 2, 3, 5 — none work, so 37 is prime.