Are all numbers ending in three zeros divisible by 2,4,8,5,and 10..verify with examples

Yes, numbers that end in three zeros are divisible by 2, 4, 8, 5, and 10. Here's a breakdown with reasoning and examples:

### 1. **Divisibility by 2**:
- A number is divisible by 2 if its last digit is even.
- If a number ends in three zeros (e.g., 1000, 2000), it obviously ends with an even number (0), so it is divisible by 2.

### 2. **Divisibility by 4**:
- A number is divisible by 4 if the last two digits are divisible by 4.
- Any number ending in "00" is divisible by 4 (e.g., 1000, 4000), because 00 ÷ 4 = 0.

### 3. **Divisibility by 8**:
- A number is divisible by 8 if the last three digits are divisible by 8.
- Since a number ending in three zeros is essentially "000," which is divisible by 8 (e.g., 1000 ÷ 8 = 125), the whole number is divisible by 8.

### 4. **Divisibility by 5**:
- A number is divisible by 5 if its last digit is 0 or 5.
- Numbers ending in three zeros clearly end in 0, so they are divisible by 5.

### 5. **Divisibility by 10**:
- A number is divisible by 10 if its last digit is 0.
- Again, numbers ending in three zeros satisfy this condition, so they are divisible by 10.

### Example 1: \( 1000 \)
- \( 1000 \div 2 = 500 \) (divisible by 2)
- \( 1000 \div 4 = 250 \) (divisible by 4)
- \( 1000 \div 8 = 125 \) (divisible by 8)
- \( 1000 \div 5 = 200 \) (divisible by 5)
- \( 1000 \div 10 = 100 \) (divisible by 10)

### Example 2: \( 5000 \)
- \( 5000 \div 2 = 2500 \) (divisible by 2)
- \( 5000 \div 4 = 1250 \) (divisible by 4)
- \( 5000 \div 8 = 625 \) (divisible by 8)
- \( 5000 \div 5 = 1000 \) (divisible by 5)
- \( 5000 \div 10 = 500 \) (divisible by 10)

In conclusion, any number ending in three zeros will always be divisible by 2, 4, 8, 5, and 10.

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Do you want more details on any part of the explanation, or have any questions?

Here are 5 related questions:
1. What about numbers ending in fewer zeros? Are they still divisible by these numbers?
2. How do we check divisibility by other numbers like 3 or 9?
3. Can a number be divisible by 8 but not by 4?
4. Why are divisibility rules important in mathematics?
5. How does divisibility help in simplifying large numbers?

**Tip:** Knowing divisibility rules can help you quickly identify factors of large numbers without performing division!

Are all numbers ending in three zeros divisible by 2, 4, 8, 5, and 10? Verify with examples.

Explore why all numbers ending in three zeros are divisible by 2, 4, 8, 5, and 10, using examples like 1000 and 5000. This concept covers key divisibility rules and is suitable for students in Grades 6-8.

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