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Subtracting 2 times the last digit from the rest gives a multiple of 3. (Works because 21 is divisible by 3) 405: 40 − 5 × 2 = 40 − 10 = 30 = 3 × 10. 4: The last two digits form a number that is divisible by 4. [2] [3] 40,832: 32 is divisible by 4. If the tens digit is even, the ones digit must be 0, 4, or 8.
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
Thus, 1/54, in sexagesimal, is 1/60 + 6/60 2 + 40/60 3, also denoted 1:6:40 as Babylonian notational conventions did not specify the power of the starting digit. Conversely 1/4000 = 54/60 3, so division by 1:6:40 = 4000 can be accomplished by instead multiplying by 54 and shifting three sexagesimal places.
In the past 500 years, there was no leap day in 1700, 1800 and 1900, but 2000 had one. In the next 500 years, if the practice is followed, there will be no leap day in 2100, 2200, 2300 and 2500 ...
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);
12 (twelve) is the natural number following 11 and preceding 13. Twelve is the 3rd superior highly composite number , [ 1 ] the 3rd colossally abundant number , [ 2 ] the 5th highly composite number , and is divisible by the numbers from 1 to 4 , and 6 , a large number of divisors comparatively.
Arrange the digits 1 to 9 in order so that the first two digits form a multiple of 2, the first three digits form a multiple of 3, the first four digits form a multiple of 4 etc. and finally the entire number is a multiple of 9.
The first: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 (sequence A005408 in the OEIS). All integers are either even or odd. All integers are either even or odd. A square has even multiplicity for all prime factors (it is of the form a 2 for some a ).