Some tips in number system
- The sum of five consecutive whole numbers is always divisible by 5.
- The product of three consecutive natural numbers is always divisible by 6.
- The product of three consecutive natural numbers, the first of which is even number is always divisible by 24.
- For any natural number ‘n’, n3 – n is divisible by 6.
- Any number written in the form of 10n – 1, is divisible by 3 or 9, where ‘n’ is natural number.
- The square odd number when divided by 8 leaves remainder 1.
- For any prime number P > 3, P2 – 1 is divisible by 24.
- an + bn is always divisible by a + b, when ‘n’ is odd.
- an + bn is never divisible by a – b.
- an – bn is exactly divisible by a + b, when ‘n’ is even.
- an – bn is exactly divisible by a – b, when ‘n’ is even or odd.
- The sum of two digit number and number formed by interchanging its digits is always divisible by 11.
- The difference of two digit number and number formed by interchanging its digits is always divisible by 9