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Let $a \times b$ denote the operation of multiplication on two objects.

The object $a$ is known as the multiplier of $b$.

That is, it is the object which is to multiply the multiplicand.

Note that the nature of $a$ and $b$ has deliberately been left unspecified.

They could be, for example, numbers, matrices or more complex expressions constructed from such elements.

Also known as

In algebraic systems where multiplication is commutative, it is commonplace to treat both the multiplier and multiplicand as the same sort of object, and refer to them both as factors.

Linguistic Note

The word multiplicand means that which is to be multiplied.

The -and derives from the gerundive form of Latin verbs, expressing future necessity: that which needs to be done.