Factors and Multiples — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. The digit sum of 84 is 8 + 4 = 12. Since that is divisible by 3, so is 84.
Add the digits: 8 + 4 = 12. Since 12 is divisible by 3, the divisibility rule tells us 84 is also divisible by 3.
2. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
Every number is a factor of itself, so 42 is the last factor in the list: 1, 2, 3, 6, 7, 14, 21, 42.
3. A number is divisible by 10 if it ends in 0.
The divisibility rule for 10 is simple: if the last digit is 0, the number divides evenly by 10.
4. The GCF of 28 and 42 is 14.
The largest number that divides both 28 and 42 evenly is 14, since 28 ÷ 14 = 2 and 42 ÷ 14 = 3.
5. The factor pairs of 48 are (1,48), (2,24), (3,16), (4,12), and (6,8).
6 × 8 = 48, so (6, 8) is the last factor pair. After 6, the next factor would be 8, which pairs with 6.
6. The smallest factor of any number greater than 0 is always 1.
1 divides every whole number with no remainder, making it the smallest possible factor of any number.
7. The LCM of 12 and 15 is 60.
Multiples of 15 are 15, 30, 45, 60... and multiples of 12 are 12, 24, 36, 48, 60... The smallest they share is 60.
8. 90 is divisible by 2, 3, 5, 9, and 10.
90 ends in 0, so it is divisible by 10 (90 ÷ 10 = 9). That makes 10 another factor of 90.
9. The number 56 has 8 factors in all.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56 -- count them up and you get 8 factors total.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each number pair to its GCF.
GCF of 18 and 27
→ 9
10
GCF of 20 and 50
→ 10
7
GCF of 14 and 35
→ 7
8
GCF of 24 and 32
→ 8
9
Correct matches: GCF of 18 and 27 → 9; GCF of 20 and 50 → 10; GCF of 14 and 35 → 7; GCF of 24 and 32 → 8.