Hard-3 challenges fourth graders with multiple-choice items that demand real number-theory reasoning: the GCF of 32 and 48, which number from 18, 20, 24, and 12 has exactly six factors, the LCM of 9 and 15, and which number is divisible by both 4 and 6 but NOT by 8.
Part B fills in the missing prime in the factorization of 72, the GCF of 40 and 60, the only even prime, the LCM of 4 and 14, and how many factors 90 has in all. Solving these strengthens prime factorization fluency and the habit of testing divisibility before guessing an answer.
Style:
Factors and Multiples
Part A: Multiple Choice
Circle the best answer for each question.
1. What is the GCF of 32 and 48?
A) 4
B) 8
C) 16
D) 32
2. Which number has exactly 6 factors?
A) 18
B) 20
C) 24
D) 12
3. What is the LCM of 9 and 15?
A) 30
B) 45
C) 90
D) 135
4. Which number is divisible by both 4 and 6 but NOT by 8?
A) 24
B) 36
C) 12
D) 48
Part B: Fill in the Blank
Write the correct answer on each line.
1. The prime factorization of 72 is 2 × 2 × 2 × 3 × 3.
2. The GCF of 40 and 60 is 20.
3. The only even prime number is 2.
4. The LCM of 4 and 14 is 28.
5. The number 90 has 12 factors in all.
Factors and Multiples
★ Part A: Multiple Choice
Circle the best answer for each question.
1. What is the GCF of 32 and 48?
A) 4
B) 8
C) 16
D) 32
2. Which number has exactly 6 factors?
A) 18
B) 20
C) 24
D) 12
3. What is the LCM of 9 and 15?
A) 30
B) 45
C) 90
D) 135
4. Which number is divisible by both 4 and 6 but NOT by 8?
A) 24
B) 36
C) 12
D) 48
★ Part B: Fill in the Blank
Write the correct answer on each line.
1) The prime factorization of 72 is 2 × 2 × 2 × 3 × 3.
2) The GCF of 40 and 60 is 20.
3) The only even prime number is 2.
4) The LCM of 4 and 14 is 28.
5) The number 90 has 12 factors in all.
Ready to Practice?
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9 Questions
12-18 minutes
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