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It is divisible by 2 and by 9. [6] 342: it is divisible by 2 and by 9. 19: Add twice the last digit to the rest. (Works because (10a + b) × 2 − 19a = a + 2b; since 19 is a prime and 2 is coprime with 19, a + 2b is divisible by 19 if and only if 10a + b is.) 437: 43 + 7 × 2 = 57. Add 4 times the last two digits to the rest.
The digit sum of 2946, for example is 2 + 9 + 4 + 6 = 21. Since 21 = 2946 − 325 × 9, the effect of taking the digit sum of 2946 is to "cast out" 325 lots of 9 from it. If the digit 9 is ignored when summing the digits, the effect is to "cast out" one more 9 to give the result 12.
In mathematics, a square-free integer (or squarefree integer) is an integer which is divisible by no square number other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, 10 = 2 ⋅ 5 is square-free, but 18 = 2 ⋅ 3 ⋅ 3 is not, because 18 is divisible by 9 = 3 2. The smallest ...
This system detects all single-digit errors and around 90% [citation needed] of transposition errors. 1, 3, 7, and 9 are used because they are coprime with 10, so changing any digit changes the check digit; using a coefficient that is divisible by 2 or 5 would lose information (because 5×0 = 5×2 = 5×4 = 5×6 = 5×8 = 0 modulo 10) and thus ...
The number 18 is a harshad number in base 10, because the sum of the digits 1 and 8 is 9, and 18 is divisible by 9.; The Hardy–Ramanujan number (1729) is a harshad number in base 10, since it is divisible by 19, the sum of its digits (1729 = 19 × 91).
69 is a semiprime because it is a natural number that is the product of exactly two prime numbers (3 and 23), and it is an interprime between the numbers of 67 and 71. [1] [2] 69 is not divisible by any square number other than 1, making it a square-free integer.
Seventy-two is a pronic number, as it is the product of 8 and 9. [1] It is the smallest Achilles number, as it's a powerful number that is not itself a power. [2] 72 is an abundant number. [3] With exactly twelve positive divisors, including 12 (one of only two sublime numbers), [4] 72 is also the twelfth member in the sequence of refactorable ...
The smallest abundant number not divisible by 2 or by 3 is 5391411025 whose distinct prime factors are 5, 7, 11, 13, 17, 19, 23, and 29 (sequence A047802 in the OEIS). An algorithm given by Iannucci in 2005 shows how to find the smallest abundant number not divisible by the first k primes. [1]