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m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then ...
For example, 6 and 35 factor as 6 = 2 × 3 and 35 = 5 × 7, so they are not prime, but their prime factors are different, so 6 and 35 are coprime, with no common factors other than 1. A 24×60 rectangle is covered with ten 12×12 square tiles, where 12 is the GCD of 24 and 60.
Greatest common divisors can be computed by determining the prime factorizations of the two numbers and comparing factors. For example, to compute gcd(48, 180) , we find the prime factorizations 48 = 2 4 · 3 1 and 180 = 2 2 · 3 2 · 5 1 ; the GCD is then 2 min(4,2) · 3 min(1,2) · 5 min(0,1) = 2 2 · 3 1 · 5 0 = 12 The corresponding LCM is ...
s is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n; a deficient number is greater than the sum of its proper divisors; that is, s(n) < n; a perfect number equals the sum of its proper divisors; that is, s(n) = n; an abundant number is lesser than the sum of its proper divisors; that is, s(n) > n
In number theory, the prime omega functions and () count the number of prime factors of a natural number . Thereby (little omega) counts each distinct prime factor, whereas the related function () (big omega) counts the total number of prime factors of , honoring their multiplicity (see arithmetic function).
A Harshad number in base 10 is an integer that is divisible by the sum of its digits (when written in base 10). A005349: Factorions: 1, 2, 145, 40585, ... A natural number that equals the sum of the factorials of its decimal digits. A014080: Circular primes: 2, 3, 5, 7, 11, 13, 17, 37, 79, 113, ...
For example, a $100,000 business loan paid off in two years with a 25 percent interest rate would cost $28,091.65 in total interest. That amount is far less than the $50,000 in interest you’d ...
40 is an abundant number.. Swiss mathematician Leonhard Euler noted 40 prime numbers generated by the quadratic polynomial + +, with values =,,,...,.These forty prime numbers are the same prime numbers that are generated using the polynomial + with values of from 1 through 40, and are also known in this context as Euler's "lucky" numbers.