1000 to9999 how many digites that can be divided by 4

To determine how many numbers between 1000 and 9999 are divisible by 4, we can follow these steps:

### Step 1: Identify the range
The range of four-digit numbers is from 1000 to 9999.

### Step 2: Use the divisibility rule for 4
A number is divisible by 4 if the last two digits of the number are divisible by 4.

### Step 3: Find the first and last numbers divisible by 4 in the range
- The first four-digit number divisible by 4 is 1000.
- The last four-digit number divisible by 4 is 9996.

### Step 4: Calculate the total number of terms
We need to find how many numbers between 1000 and 9999 are divisible by 4. These numbers form an arithmetic sequence where:
- The first term \( a_1 = 1000 \)
- The common difference \( d = 4 \)

Let's find the number of terms (\( n \)) in this sequence:

\[
a_n = a_1 + (n - 1) \times d
\]

Set \( a_n = 9996 \), \( a_1 = 1000 \), and \( d = 4 \), and solve for \( n \):

\[
9996 = 1000 + (n - 1) \times 4
\]

\[
9996 - 1000 = (n - 1) \times 4
\]

\[
8996 = (n - 1) \times 4
\]

\[
n - 1 = \frac{8996}{4} = 2249
\]

\[
n = 2249 + 1 = 2250
\]

### Final Answer:
There are **2,250** four-digit numbers between 1000 and 9999 that are divisible by 4.

Would you like any additional details or have any questions?

### Related Questions:
1. How would the calculation change if the range was from 5000 to 9000?
2. What are the properties of numbers divisible by 4?
3. How many numbers between 1000 and 9999 are divisible by 3?
4. How many four-digit even numbers are there?
5. Can a number be divisible by 4 but not by 2? Why or why not?
6. What is the smallest 4-digit number divisible by both 3 and 4?
7. How do you find the greatest common divisor of two numbers?
8. How many four-digit palindromic numbers are divisible by 4?

**Tip:** For any number, if the last two digits are divisible by 4, the entire number is divisible by 4.

Discover how many four-digit numbers between 1000 and 9999 are divisible by 4. Follow a detailed step-by-step solution using the divisibility rule and arithmetic sequence formula. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation