This probability is based on the observation that the probability that any number is divisible by a prime \scriptstyle p is \scriptstyle 1/p (for example, every 7th integer is divisible by 7).
Either a or b is divisible by 3. 2. Either a or b is divisible by 4. 3. Either a or b or c is divisible by 5. 4. The product of a, b, and c is divisible by 60. 5.
For each prime p, there is a thread in the middle of the pipe that consumes a number from the pipe if that number is divisible by p. Otherwise, it passes the value on to the next thread in the pipe.
If a year is divisible by both, then it is a leap year.
As Pummy Kalsi rightly observed 4^4- 4 = 4*(4^2 + 1)*(4 – 1)*(4 + 1), which shows that 4^4-4 is divisible by 5 even without computing its actual value.
If a year is divisible by 4, but not 100, like 2012, it is a leap year.
Because the year 2000 is divisible by 400, there will be a Feb. 29 in the year 2000 even though there was not one in 1900.
If a year is divisible by 100, but not 400, like 1900, then it is NOT a leap year.
As touched on above, a year that is divisible by 100, but not by 400, is not technically a leap year.
If a year is divisible by both 4 and 100, like 2000, keep reading.
Usually a year is a leap year if it is divisible by four, like 2012, or 1992.
