Divisibility Rules for 7 and 11 The topic of this lesson focuses on understanding the unique rules of divisibility by 7 and 11. Divisibility by 7: A n...
The topic of this lesson focuses on understanding the unique rules of divisibility by 7 and 11.
Divisibility by 7:
A number is divisible by 7 if the last digit is 7 or 0.
This means the number can be written in the form of 7k or 7k + 1, where k is an integer.
Divisibility by 11:
A number is divisible by 11 if the difference between the sum of digits at odd positions and the sum of digits at even positions is equal to either 0 or 1.
This means the number can be written as 11a or 11b, where a and b are distinct digits.
Combining the Two Rules:
To determine if a number is divisible by both 7 and 11, we need to check both its last digit and the difference between its odd and even digit sums.
If the last digit is 7 and the difference between odd and even digits is 0 or 1, the number is divisible by both 7 and 11.
Examples:
7 is divisible by 7 because its last digit is 7.
14 is divisible by 11 because the difference between the odd and even digits (1 and 4) is 3, which is divisible by 11.
28 is divisible by both 7 and 11 because its last digit is 8 and the difference between its odd and even digits (2 and 8) is 6, which is divisible by 11.
55 is divisible by neither 7 nor 11 because it has a last digit of 5 and the difference between its odd and even digits is 4, which is not divisible by either 7 or 11