Divisibility Rule of 496

The divisibility rule for 496 is a method by which we can find out if a number is divisible by 496 without using traditional division. Let's check if 992 is divisible by 496 using this rule.
 

Step 1: Since 496 is a composite number, first check divisibility by its prime factors, which are 2, 2, 2, 31 (since 496 = 2^4 × 31).
 

Step 2: Check for divisibility by 16 (2^4). The last four digits of the number (0992) should be divisible by 16. 992 ÷ 16 = 62, which is a whole number.
 

Step 3: Check for divisibility by 31. Use the divisibility rule for 31: Multiply the last digit by 3, add the result to the rest of the number, and check if the sum is a multiple of 31. For 992, multiply the last digit (2) by 3, giving 6, and add this to the rest of the number (99), resulting in 105. 105 ÷ 31 is not a whole number, so 992 is not divisible by 31.
 

Since 992 is not divisible by 31, it is not divisible by 496 either.
 

Understanding and mastering the divisibility rules can significantly aid in mathematical calculations. Here are some tips and tricks for the divisibility rule of 496:
 

• Know the prime factorization: Remember the prime factorization of 496 as 2^4 × 31, which helps check divisibility by smaller components.
   
• Use divisibility by powers of 2: Learn the rules for divisibility by powers of 2 (e.g., 4, 8, 16) to simplify checking larger numbers.
   
• Practice the rule for 31: Familiarize yourself with the divisibility rule for 31 to quickly assess larger numbers.
   
• Repeat the process for large numbers: For large numbers, break them down and check divisibility by smaller factors sequentially.
   
• Verify using division: After applying the rule, use actual division to verify your results and strengthen your understanding.
   

• Divisibility rule: A set of guidelines to determine if one number is divisible by another without performing division.
   
• Prime factorization: Breaking down a number into its prime number components.
   
• Composite number: A positive integer with more than two distinct positive divisors.
   
• Multiples: The result of multiplying one integer by another.
   
• Integer: A whole number that can be positive, negative, or zero.