Numbers are categorized in various sets based on their properties.
Divisibility of Numbers
Number divisible by 2
Units digit – 0, 2, 4, 6, 8
Example: 42, 66, 98, 1124
Number divisible by 3
Sum of digits is divisible by 3
Example: 267 --- (2 + 6 + 7) = 15
15 is divisible by 3
Number divisible by 4
Number formed by the last two digits is divisible by 4
Example: 832
The last two digits is divisible by 4, hence 832 is divisible by 4
Number divisible by 5
Units digit is either zero or five
Example: 50, 20, 55, 65, etc
Number divisible by 6
The number is divisible by both 2 and 3
Example: In 168 Last digit = 8 ---- (8 is divisible by 2)
Sum of digits = (1 + 6 + 8) = 15 ----- (divisible by 3)>/p>
Hence, 168 is divisible by 6
Number divisible by 11
If the difference between the sums of the digits at even places and the sum of digits at odd places is either 0 or divisible by 11.
Example: 4527039
Digits on even places: 4 + 2 + 0 + 9 =15
Digits on odd places: 5 + 7 + 3 = 15
Difference between odd and even = 0
Therefore, number is divisible by 11
Number divisible by 12
The number is divisible by both 4 and 3
Example: 1932
Last two digits divisible by 4
Sum of digits = (1 + 9 + 3 + 2) = 15 ---- (Divisible by 3)
Hence, the number 1932 is divisible by 12