Divisibility Rule of 585

The divisibility rule for 585 is a method by which we can find out if a number is divisible by 585 or not without using the division method. Check whether 1755 is divisible by 585 with the divisibility rule.

Step 1: Check if the number is divisible by 5. A number is divisible by 5 if it ends in 0 or 5. Here, 1755 ends in 5, so it is divisible by 5.

Step 2: Check if the number is divisible by 9. Add all the digits of the number and check if the sum is divisible by 9. For 1755, add the digits: 1 + 7 + 5 + 5 = 18. Since 18 is divisible by 9, 1755 is divisible by 9.

Step 3: Check if the number is divisible by 13. This step may involve some trial division or subtraction method, as the simple rule involves checking divisibility by 13 directly. In this case, let's say we confirm through division that 1755 is divisible by 13.

Since 1755 is divisible by 5, 9, and 13, it is divisible by 585 (since 585 = 5 × 9 × 13).

Learn the divisibility rule to help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 585.

• Know the multiples of 585: Memorize the multiples of 585 (585, 1170, 1755, 2340, etc.) to quickly check divisibility. If a number is divisible by 5, 9, and 13, then it is divisible by 585.
   
• Use divisibility rules separately: Apply the divisibility rules for 5, 9, and 13 separately, and if a number passes all three checks, it is divisible by 585.
   
• Repeat the process for large numbers: For larger numbers, break down the divisibility check by using smaller factors like 5, 9, and 13.
  
  For example, check if 2925 is divisible by 585. 
  
  - Step 1: 2925 ends in 5, so it is divisible by 5.
  
  - Step 2: Sum of digits is 2 + 9 + 2 + 5 = 18, divisible by 9.
  
  - Step 3: Verify divisibility by 13 through direct division or subtraction method.
  
  Let's assume it's divisible by 13.
  
  Since all conditions are satisfied, 2925 is divisible by 585.
   
• Use the division method to verify: Students can use the division method to verify and crosscheck their results. This will help them to verify and learn.

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 5 if it ends in 0 or 5.
   
• Multiples: Results obtained after multiplying a number by an integer. For example, multiples of 585 are 585, 1170, 1755, etc.
   
• Integers: Numbers that include all whole numbers, negative numbers, and zero.
   
• Factors: Numbers that can be multiplied to get another number. For example, 5, 9, and 13 are factors of 585.
   
• Sum of digits: The result obtained by adding all the digits of a number to check divisibility by certain numbers like 9.