Divisibility Rule of 284

The divisibility rule for 284 is a method by which we can find out if a number is divisible by 284 or not without using the division method. Check whether 568 is divisible by 284 with the divisibility rule.

Step 1: Since 284 is a composite number, it can be broken down into its prime factors for simpler checking. The prime factors of 284 are 2 and 71 (284 = 2 × 2 × 71). Therefore, a number divisible by 284 must be divisible by both 4 (2×2) and 71.

Step 2: First, check divisibility by 4. For 568, look at the last two digits, 68. Since 68 is divisible by 4, we proceed to the next step.

Step 3: Check divisibility by 71. Divide 568 by 71. Since 568 ÷ 71 = 8 without a remainder, 568 is divisible by 71.

Step 4: Since 568 is divisible by both 4 and 71, it is also divisible by 284.

• Know the multiples of 284: Memorize the multiples of 284 (284, 568, 852…etc.) to quickly check the divisibility. If a number is a multiple of 284, it is divisible by 284.
   
• Break down into factors: Use the prime factors of 284 (2, 2, 71) to simplify the process. If a number is divisible by 4 and 71, it is divisible by 284.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process with smaller components until they reach a conclusion. 
   
• Use the division method to verify: Students can use the division method to verify and cross-check their results. This helps in learning and confirming the accuracy of results.
   

• Divisibility rule: The set of rules used to determine if a number is divisible by another number without performing division.
   
• Prime factors: The prime numbers that multiply together to give a composite number. For 284, the prime factors are 2 and 71.
   
• Multiples: The results obtained by multiplying a number by integers. For example, multiples of 284 are 284, 568, and 852.
   
• Subtraction: A mathematical process of finding the difference between two numbers.
   
• Verification: The process of confirming the accuracy of a result, often by using a different method such as actual division.