Divisibility by 11 Solution Explained

To determine if a number is divisible by 11, we use the divisibility rule for 11. This rule involves calculating the alternating sum of the digits.

Divisibility Rule for 11: A number is divisible by 11 if the difference between the sum of the digits at the odd places (starting from the right) and the sum of the digits at the even places (starting from the right) is either 0 or a multiple of 11 (like 11, 22, etc.).

Testing Number Divisibility by 11

Let's apply this rule to each given number:

• Number: $502579$
  
  • Sum of digits at odd places (1st, 3rd, 5th from right): $9 + 5 + 0 = 14$
  • Sum of digits at even places (2nd, 4th, 6th from right): $7 + 2 + 5 = 14$
  • Difference: $14 - 14 = 0$
  Since the difference is 0, 502579 is divisible by 11.
• Number: $513589$
  
  • Sum of digits at odd places: $9 + 5 + 1 = 15$
  • Sum of digits at even places: $8 + 3 + 5 = 16$
  • Difference: $15 - 16 = -1$
  Since -1 is not 0 or a multiple of 11, 513589 is not divisible by 11.
• Number: $502589$
  
  • Sum of digits at odd places: $9 + 5 + 0 = 14$
  • Sum of digits at even places: $8 + 2 + 5 = 15$
  • Difference: $14 - 15 = -1$
  Since -1 is not 0 or a multiple of 11, 502589 is not divisible by 11.
• Number: $512579$
  
  • Sum of digits at odd places: $9 + 5 + 1 = 15$
  • Sum of digits at even places: $7 + 2 + 5 = 14$
  • Difference: $15 - 14 = 1$
  Since 1 is not 0 or a multiple of 11, 512579 is not divisible by 11.

Conclusion

Based on the divisibility rule for 11, the number 502579 yields a difference of 0, confirming it is divisible by 11.