Page 2 - Lesson Note

Number Sum of the digits Sum of the digits Difference
(at odd places) (at even places)
from the right from the right
61809 9 + 8 + 6 = 23 0 + 1 =1 23-1 = 22

Therefore, 61809 is divisible by 11.

Divisibility by 12: A number is divisible by 12 if it is divisible by both 3 and 4.

Ex- 168, 1 + 6 + 8 =15 is divisible by 3 and last two digit i.e. 68 is
divisible by 4.
Therefore 168 is divisible by 12.

Divisibility by 15: A number is divisible by 15 if it is divisible by both 3 and 5.

Ex- 315, 3 + 1 + 5 = 9 is divisible by 3 and the last digit of the number is 5
hence it is divisible with 5 also.
Therefore 168 is divisible by 15.

More Divisibility Rules:
 If a number is divisible by another number then it is divisible by each of the
factors of that number. Ex- 24
 If a number is divisible by two co-prime numbers then it is divisible by their
product also.
Ex- The number 80 is divisible by 4 and 5. It is also divisible by 4 × 5 = 20,
and 4 and 5 are co-primes.
 If two given numbers are divisible by a number, then their sum is also divisible
by that number.
Ex- The numbers 16 and 20 are both divisible by 4. The number 16 + 20 =
36 is also divisible by 4.
 If two given numbers are divisible by a number, then their difference is also
divisible by that number.
Ex- The numbers 35 and 20 are both divisible by 5. Is their difference 35 –
20 = 15 also divisible by 5.