Divisibility Rule of 825

The divisibility rule for 825 is a method by which we can find out if a number is divisible by 825 or not without using the division method. Check whether 4950 is divisible by 825 with the divisibility rule.  

Step 1: Check divisibility by 5. A number is divisible by 5 if it ends in 0 or 5. In 4950, the last digit is 0, so it is divisible by 5.

Step 2: Check divisibility by 3. Add the digits of the number: 4+9+5+0=18. Since 18 is divisible by 3, 4950 is also divisible by 3.

Step 3: Check divisibility by 11. Subtract the sum of alternate digits: (4+5)-(9+0)=9-9=0. Since 0 is divisible by 11, 4950 is divisible by 11.

Step 4: Since 4950 is divisible by 5, 3, and 11, it is also divisible by 825 (5×3×11=825).

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 825.

Know the prime factorization of 825:

825 = 5 × 3 × 11 × 5. A number must be divisible by all these factors to be divisible by 825.

Use the divisibility rules for 5, 3, and 11:

   - For 5: Check if the number ends in 0 or 5.
   - For 3: Check if the sum of the digits is divisible by 3.
   - For 11: Subtract the sum of the digits in odd positions from the sum of the digits in even positions. If the result is 0 or a multiple of 11, the number is divisible by 11.

Check for large numbers:

   If the number is large, break it down by checking divisibility for each factor separately (5, 3, and 11).

Use the division method to verify: 

Students can use the division method as a way to verify and cross-check their results. This will help them verify and also learn.
 

• Divisibility rule: The set of rules used to determine whether a number is divisible by another number or not.
   
• Prime factorization: Breaking down a number into its prime factors, which are prime numbers that multiply together to make the original number.
   
• Multiple: The result of multiplying a number by an integer. For example, multiples of 5 are 5, 10, 15, etc.
   
• Sum of digits: Adding all the digits in a number to check divisibility by certain numbers like 3.
   
• Alternate digits subtraction: Subtracting the sum of alternate digits to check divisibility, used for 11.