Factors and Multiples — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. 36 has 5 factor pairs in all.
Factor pairs of 36: (1,36), (2,18), (3,12), (4,9), (6,6) — 5 pairs total.
2. The factors of 28 are 1, 2, 4, 7, 14, and 28.
Every number is a factor of itself. 28 ÷ 28 = 1.
3. 72 is divisible by 2, 3, and 9 because it ends in 2 and its digit sum is 9.
Digit sum of 72 = 7+2 = 9, which is divisible by both 3 and 9.
4. The factor pairs of 18 are (1,18), (2,9), and (3,6).
3 × 6 = 18, so 3 completes the third factor pair.
5. A number divisible by both 2 and 5 must end in 0.
A number divisible by 2 ends in an even digit; divisible by 5 ends in 0 or 5. The only overlap is 0.
6. 48 ÷ 6 = 8, so 6 and 8 are both factors of 48.
If A ÷ B = C with no remainder, then B and C are both factors of A.
7. The digit sum of 123 is 1 + 2 + 3 = 6. Since that is divisible by 3, so is 123.
1 + 2 + 3 = 6. Since 6 ÷ 3 = 2, the digit sum rule confirms 123 is divisible by 3.
8. The largest factor of any number is the number itself.
Every number divides itself exactly once, making it its own largest factor.
9. The factor pairs of 40 are (1,40), (2,20), (4,10), and (5,8).
5 × 8 = 40, so 8 completes the fourth factor pair of 40.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
16
→ 5 factors
2 factors
23
→ 2 factors
6 factors
30
→ 8 factors
5 factors
12
→ 6 factors
8 factors
16 → 5 factors (1,2,4,8,16); 23 → 2 factors (1,23 — prime); 30 → 8 factors (1,2,3,5,6,10,15,30); 12 → 6 factors (1,2,3,4,6,12).