31×59

31×59 denotes the product of the integers 31 and 59. The result is 1829, an odd four-digit number. Both factors are prime, so 1829 is a semiprime and has exactly four positive divisors: 1, 31, 59, and 1829.

The product can be computed in several straightforward ways. Using distributivity: 31×59 = (30+1)×59 = 1770+59 = 1829. Equivalently, 59×31 = (60−1)×31 = 1860−31 = 1829. These methods illustrate common algebraic techniques for simplifying multiplication.

In number theory, semiprimes like 1829 are defined as numbers that are the product of exactly two prime factors (counting multiplicities). Since 1829 = 31×59, its prime factorization consists of two distinct primes. This makes it a simple example used in introductory discussions of factorization and primality.

Applications and context: 31×59 appears in basic arithmetic and serves as a representative case for practicing multiplication, factorization, and the concept of semiprimes. It also provides a concrete instance of how the distributive property can simplify calculations.