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The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n. The tables show the multiplicity for each prime factor. ... 48: 2 4 ·3 ...
Since the greatest prime factor of 48 2 + 1 = 2305 is 461, which is clearly more than twice 48, 48 is a Størmer number. [ 11 ] 48 is a Harshad number in decimal, [ 12 ] as it is divisible by 4+8 = 12.
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...
2.48 Pythagorean primes. ... (or prime) is a natural number ... write the prime factorization of n in base 10 and concatenate the factors; iterate until a prime is ...
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 ...
The sequence of highly composite numbers (sequence A002182 in the OEIS) is a subset of the sequence of smallest numbers k with exactly n divisors (sequence A005179 in the OEIS). Highly composite numbers whose number of divisors is also a highly composite number are. 1, 2, 6, 12, 60, 360, 1260, 2520, 5040, 55440, 277200, 720720, 3603600 ...
Since q is a factor of 2 p − 1, for all positive integers c, q is also a factor of 2 pc − 1. Since p is prime and q is not a factor of 2 1 − 1, p is also the smallest positive integer x such that q is a factor of 2 x − 1. As a result, for all positive integers x, q is a factor of 2 x − 1 if and only if p is a factor of x.
A simple formula is. for positive integer , where is the floor function, which rounds down to the nearest integer. By Wilson's theorem, is prime if and only if . Thus, when is prime, the first factor in the product becomes one, and the formula produces the prime number . But when is not prime, the first factor becomes zero and the formula ...