In simple algebra, multiplication is the process of calculating the result when a number called the product of , or simply
and
, and each of the numbers
. The symbol
and
is taken
is called a factor of the product
times. The result of a multiplication is . Multiplication is denoted
,
,
is known as the multiplication sign. Normal multiplication is associative, commutative, and distributive.
More generally, multiplication can also be defined for other mathematical objects such as groups, matrices, sets, and tensors.
Karatsuba and Ofman (1962) discovered that multiplication of two algorithm now known as Karatsuba multiplication.
digit numbers can be done with a bit complexity of less than
using an