Answer:
- factor: a submultiple; an integer value that gives an integer quotient when the number is divided by it.
- multiple: the product of the number and another integer
Explanation:
Factors
A set of factors of a number (N) is a set of integers {f1, f2, f3, ...} whose product is the number:
f1 × f2 × f3 × ... = N
Often the term "factors" is used to mean "prime factors," the set of prime numbers whose product is N.
When N = 25, the prime factors are {5, 5}. That is ...
5×5 = 25
__
Divisors
A "divisor" of a number is a sub-multiple of N. That is, the quotient N/k is an integer for some divisor k of N. Usually, we're interested in integer divisors. All prime factors will be integer divisors of N. The term "factor" is often used when the term "divisor" is meant.
Divisors of N = 25 include 1, 5, and 25. There will be an odd number of integer divisors (as here) if the number N is a perfect square.
__
Multiples
For an integer k, the value k×N is called a multiple of N, often, the k-th multiple of N.
Multiples of 25 include 25, 50, 75, 100, 125, and any other decimal number ending in 25, 50, 75, or 00.
__
Another example
When N=30, the prime factors are {2, 3, 5}. The divisors are {1, 2, 3, 5, 6, 10, 15, 30}. (Note there are an even number of divisors.) Multiples of 30 include 30, 60, 90, 120, ....