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That is, although 360 and 2520 both have more divisors than any number twice themselves, 2520 is the lowest number divisible by both 1 to 9 and 1 to 10, whereas 360 is not the lowest number divisible by 1 to 6 (which 60 is) and is not divisible by 1 to 7 (which 420 is).
The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; [2] [3] this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4. If any number ends in a two digit number that ...
Later, on a calendar yet to come (we'll get to it), it was decreed that years divisible by 100 not follow the four-year leap day rule un ... 1800 and 1900, but 2000 had one. In the next 500 years ...
Mar 30 17 Apr 9: Apr 17 18 Mar 29: Apr 7 19 Apr 17: ... 20 indicates that 2000 is a leap year. ... Gregorian calendar – all years divisible by 100, ...
In the Gregorian calendar, the standard civil calendar used in most of the world, February 29 is added in each year that is an integer multiple of four, unless it is evenly divisible by 100 but not by 400. For example, 1900 was not a leap year, but 2000 was.
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
the k given prime numbers p i must be precisely the first k prime numbers (2, 3, 5, ...); if not, we could replace one of the given primes by a smaller prime, and thus obtain a smaller number than n with the same number of divisors (for instance 10 = 2 × 5 may be replaced with 6 = 2 × 3; both have four divisors);
It is only necessary to work through the complete function when calculating the length of February in a year which is divisible by 100 without remainder. When calculating the length of February in any other year it is only necessary to evaluate the terms to the left of the fifth + sign.