2×3×11

2×3×11 is a mathematical expression representing the product of three prime numbers: 2, 3, and 11. The result of this multiplication is 66. This specific product is notable in certain contexts, particularly in number theory and recreational mathematics.

The number 66, derived from 2×3×11, is a composite number, meaning it has divisors other than 1 and itself. Its prime factorization is precisely 2×3×11. This makes 66 a sphenic number, a type of composite number that is the product of three distinct prime numbers.

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. The expression 2×3×11 can be seen as the fundamental building block of the number 66 in terms of its prime components. This decomposition is unique due to the fundamental theorem of arithmetic, which states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers, and that, moreover, this representation is unique, apart from the order of the factors.

In various mathematical puzzles or problems, identifying numbers that are products of specific sets of primes, like 2×3×11, can be a useful skill. The sequence of prime numbers is infinite, and their products generate a vast array of composite numbers with diverse properties. The expression 2×3×11 is a simple yet illustrative example of this principle.