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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 ...
Informally, the probability that any number is divisible by a prime (or in fact any integer) p is ; for example, every 7th integer is divisible by 7. Hence the probability that two numbers are both divisible by p is 1 p 2 , {\displaystyle {\tfrac {1}{p^{2}}},} and the probability that at least one of them is not is 1 − 1 p ...
[1] [2] Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. [3] [4] E.g., the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7 but the integers 2 and 3 are not because each can only be divided by one and itself.
Prime numbers have exactly 2 divisors, and highly composite numbers are in bold. 7 is a divisor of 42 because =, so we can say It can also be said that 42 is divisible by 7, 42 is a multiple of 7, 7 divides 42, or 7 is a factor of 42. The non-trivial divisors of 6 are 2, −2, 3, −3.
For example, 6 is highly composite because d(6)=4 and d(n)=1,2,2,3,2 for n=1,2,3,4,5 respectively. A related concept is that of a largely composite number , a positive integer that has at least as many divisors as all smaller positive integers.
To factorize a small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division: checking if the number is divisible by prime numbers 2, 3, 5, and so on, up to the square root of n. For larger numbers, especially when using a computer, various more sophisticated factorization algorithms are more efficient.
An integer is determined to be even if it is divisible by two. When written in base 10, all multiples of 2 will end in 0, 2, 4, 6, or 8. [3] 2 is the smallest and the only even prime number, and the first Ramanujan prime. [4] It is also the first superior highly composite number, [5] and the first colossally abundant number. [6]
In mathematics a polydivisible number (or magic number) is a number in a given number base with digits abcde... that has the following properties: [1] Its first digit a is not 0. The number formed by its first two digits ab is a multiple of 2. The number formed by its first three digits abc is a multiple of 3.
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