Divisibility Rules Worksheets - Math Monks - Free Printable

To solve the problem, we need to determine which numbers in each section are divisible by the given numbers. Let's go through each section step by step.

---

1. Divisible by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

#### Numbers:
- 345: \(3 + 4 + 5 = 12\) (divisible by 3) → Circle
- 1,345: \(1 + 3 + 4 + 5 = 13\) (not divisible by 3)
- 4,578: \(4 + 5 + 7 + 8 = 24\) (divisible by 3) → Circle
- 76: \(7 + 6 = 13\) (not divisible by 3)
- 3,467: \(3 + 4 + 6 + 7 = 20\) (not divisible by 3)
- 96: \(9 + 6 = 15\) (divisible by 3) → Circle
- 27: \(2 + 7 = 9\) (divisible by 3) → Circle
- 165: \(1 + 6 + 5 = 12\) (divisible by 3) → Circle
- 178: \(1 + 7 + 8 = 16\) (not divisible by 3)
- 268: \(2 + 6 + 8 = 16\) (not divisible by 3)
- 1,349: \(1 + 3 + 4 + 9 = 17\) (not divisible by 3)
- 456: \(4 + 5 + 6 = 15\) (divisible by 3) → Circle
- 346: \(3 + 4 + 6 = 13\) (not divisible by 3)
- 3,469: \(3 + 4 + 6 + 9 = 22\) (not divisible by 3)

Circled numbers: 345, 4,578, 96, 27, 165, 456

---

2. Divisible by 5

A number is divisible by 5 if it ends in 0 or 5.

#### Numbers:
- 35: Ends in 5 → Circle
- 1,400: Ends in 0 → Circle
- 34: Does not end in 0 or 5
- 46: Does not end in 0 or 5
- 105: Ends in 5 → Circle
- 225: Ends in 5 → Circle
- 127: Does not end in 0 or 5
- 245: Ends in 5 → Circle
- 200: Ends in 0 → Circle
- 50: Ends in 0 → Circle
- 19: Does not end in 0 or 5
- 27: Does not end in 0 or 5
- 30: Ends in 0 → Circle
- 100: Ends in 0 → Circle

Circled numbers: 35, 1,400, 105, 225, 245, 200, 50, 30, 100

---

3. Divisible by 2

A number is divisible by 2 if it is even (ends in 0, 2, 4, 6, or 8).

#### Numbers:
- 24: Even → Circle
- 100: Even → Circle
- 127: Odd
- 130: Even → Circle
- 1,000: Even → Circle
- 82: Even → Circle
- 170: Even → Circle
- 123: Odd
- 137: Odd
- 144: Even → Circle
- 204: Even → Circle
- 275: Odd
- 375: Odd
- 122: Even → Circle

Circled numbers: 24, 100, 130, 1,000, 82, 170, 144, 204, 122

---

4. Divisible by 2 and 5

A number is divisible by both 2 and 5 if it ends in 0.

#### Numbers:
- 3,290: Ends in 0 → Circle
- 9,200: Ends in 0 → Circle
- 7,571: Does not end in 0
- 5,370: Ends in 0 → Circle
- 2,011: Does not end in 0
- 67: Does not end in 0
- 120: Ends in 0 → Circle
- 145: Does not end in 0
- 200: Ends in 0 → Circle
- 105: Does not end in 0
- 22: Does not end in 0
- 30: Ends in 0 → Circle
- 10: Ends in 0 → Circle
- 144: Does not end in 0

Circled numbers: 3,290, 9,200, 5,370, 120, 200, 30, 10

---

5. Divisible by 5 and 10

A number is divisible by both 5 and 10 if it ends in 0.

#### Numbers:
- 20: Ends in 0 → Circle
- 102: Does not end in 0
- 25: Does not end in 0
- 100: Ends in 0 → Circle
- 1,020: Ends in 0 → Circle
- 1,050: Ends in 0 → Circle
- 60: Ends in 0 → Circle
- 145: Does not end in 0
- 2,452: Does not end in 0
- 2,455: Does not end in 0
- 204: Does not end in 0
- 132: Does not end in 0
- 2,495: Does not end in 0
- 3,050: Ends in 0 → Circle

Circled numbers: 20, 100, 1,020, 1,050, 60, 3,050

---

Final Answer

\[
\boxed{
\begin{array}{l}
\text{Divisible by 3: } 345, 4,578, 96, 27, 165, 456 \\
\text{Divisible by 5: } 35, 1,400, 105, 225, 245, 200, 50, 30, 100 \\
\text{Divisible by 2: } 24, 100, 130, 1,000, 82, 170, 144, 204, 122 \\
\text{Divisible by 2 and 5: } 3,290, 9,200, 5,370, 120, 200, 30, 10 \\
\text{Divisible by 5 and 10: } 20, 100, 1,020, 1,050, 60, 3,050 \\
\end{array}
}
\]