Learn about divisibility through these example problems with detailed step-by-step solutions.
Example 1: Checking Divisibility by 2
Is 346 divisible by 2?
Step 1: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
Step 2: The number is 346. The last digit is 6.
Step 3: Since 6 is an even number, 346 is divisible by 2.
Step 4: Therefore, 346 is divisible by 2.
Example 2: Checking Divisibility by 3
Is 729 divisible by 3?
Step 1: A number is divisible by 3 if the sum of its digits is divisible by 3.
Step 2: The number is 729. Sum the digits: \(7 + 2 + 9\).
Step 3: Calculate: \(7 + 2 = 9\), \(9 + 9 = 18\).
Step 4: Check if 18 is divisible by 3: \(18 \div 3 = 6\), which is an integer.
Step 5: Therefore, 729 is divisible by 3.
Example 3: Checking Divisibility by 6
Is 852 divisible by 6?
Step 1: A number is divisible by 6 if it is divisible by both 2 and 3.
Step 2: Check divisibility by 2: The number is 852, and the last digit is 2 (even), so it is divisible by 2.
Step 3: Check divisibility by 3: Sum the digits: \(8 + 5 + 2 = 15\).
Step 4: Check if 15 is divisible by 3: \(15 \div 3 = 5\), which is an integer.
Step 5: Since 852 is divisible by both 2 and 3, it is divisible by 6.
Step 6: Therefore, 852 is divisible by 6.
Practice Mode
Enter your own problem related to divisibility, and get a step-by-step solution.
Note: This basic solver can currently handle divisibility checks for numbers by 2, 3, 4, 5, 6, 9, or 10 (e.g., Is 346 divisible by 2? Is 729 divisible by 3?). Enter the number and divisor clearly.
Related Concepts
Explore these related mathematical concepts to deepen your understanding of divisibility.
Divisibility Rules
Rules help determine if a number is divisible by another without performing division.
Factors
A number is divisible by its factors, which are numbers that divide it evenly.
Prime Numbers
Prime numbers are divisible only by 1 and themselves, key to understanding divisibility.
Multiples
If a number is divisible by another, it is a multiple of that number.
