Divisibility Rule of 693

The divisibility rule for 693 is a method by which we can find out if a number is divisible by 693 or not without using the division method. Check whether 1386 is divisible by 693 using the divisibility rule.
 

Step 1: Break down 693 into its prime factors: 693 = 3 × 3 × 7 × 11.

Step 2: Check if the number is divisible by each of these factors.
 

To check divisibility by 3, ensure the sum of the digits is divisible by 3.

For 1386, 1 + 3 + 8 + 6 = 18, which is divisible by 3.
 

To check divisibility by 7, follow the specific rule for 7 (as described earlier).

For 1386, double the last digit (6): 6 × 2 = 12. Subtract from the remaining number: 138 - 12 = 126. Since 126 is divisible by 7, 1386 passes this test.
 

To check divisibility by 11, see if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is a multiple of 11.

For 1386, (1 + 8) - (3 + 6) = 9 - 9 = 0, which is a multiple of 11.
 

Since 1386 is divisible by 3, 7, and 11, it is divisible by 693.
 

• Know the prime factors: Memorize the prime factors of 693 (3, 7, and 11) to quickly check divisibility.
   
• Use the divisibility rules for each factor: Familiarize yourself with the divisibility rules for 3, 7, and 11, as these will help you determine if a number is divisible by 693.
   
• Verify by division: Once you determine divisibility by 3, 7, and 11, you can verify your result by dividing the original number by 693 to ensure no remainder.
   
• Practice: Regular practice with different numbers will help you become proficient in applying the divisibility rule for 693.
   
• Simplify large numbers: Break down large numbers into smaller parts to check divisibility more easily.
   

• Divisibility Rule: The set of rules used to determine if a number is divisible by another without direct division.
   
• Prime Factors: The prime numbers that multiply together to give the original number. For 693, these are 3, 7, and 11.
   
• Multiples: Numbers obtained by multiplying a number by integers. For example, multiples of 693 include 693, 1386, etc.
   
• Sum of Digits: The total when adding all digits of a number, used to check divisibility by 3.
   
• Alternating Sum: The difference between the sum of digits in odd positions and even positions, used for checking divisibility by 11.