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The original number is divisible by 7 if and only if the number obtained using this procedure is divisible by 7. For example, the number 371: 37 − (2×1) = 37 − 2 = 35; 3 − (2 × 5) = 3 − 10 = −7; thus, since −7 is divisible by 7, 371 is divisible by 7. Similarly a number of the form 10x + y is divisible by 7 if and only if x + 5y ...
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21). If m is a divisor of n, then so is −m. The tables below only ...
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.
Note: Numbers in bold are themselves highly composite numbers. Only the twentieth highly composite number 7560 (= 3 × 2520) is absent. 10080 is a so-called 7-smooth number (sequence A002473 in the OEIS ) .
In number theory, a weird number is a natural number that is abundant but not semiperfect. [ 1 ] [ 2 ] In other words, the sum of the proper divisors ( divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number itself.
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 ...
First, the digits of the number being tested are grouped in blocks of three. The odd numbered groups are summed. The sum of the even numbered groups is then subtracted from the sum of the odd numbered groups. The test number is divisible by 7, 11 or 13 iff the result of the summation is divisible by 7, 11 or 13 respectively. [2] [3] Example:
5040 (five thousand [and] forty) is the natural number following 5039 and preceding 5041.. It is a factorial (7!), the 8th superior highly composite number, [1] the 19th highly composite number, [2] an abundant number, the 8th colossally abundant number [3] and the number of permutations of 4 items out of 10 choices (10 × 9 × 8 × 7 = 5040).