Factors and Multiples
Factors and multiples are both to do with multiplication:

Here are the details:
Factors
"Factors" are the numbers you can multiply together to get another number:
2 and 3 are factors of 6
A number can have many factors.
Example: 3 and 4 are factors of 12, because 3×4=12
Also 2×6=12 so 2 and 6 are also factors of 12,
And 1×12=12 so 1 and 12 are factors of 12 as well.
AND because multiplying negatives makes a positive, 1, 2, 3, 4, 6 and 12 are also factors of 12
Like this: (1) × (12) = 12, (2) × (6) = 12, (3) × (4) = 12
So ALL the factors of 12 are 1, 2, 3, 4, 6 and 12 AND 1,2,3,4,6 and 12
Learn about Greatest Common Factor and how to find All Factors of a Number.
Multiples
A multiple is the result of multiplying a number by an integer (not a fraction).
Examples:
Multiples of 3:
12 is a multiple of 3, because 3 × 4 = 12
3 is a multiple of 3, because 3 × 1 = 3
Multiples of 5:
10 is a multiple of 5, because 5 × 2 = 10
But 11 is NOT a multiple of 5
So you must multiply by an integer, but the number that is being multiplied can be anything.
Example: Multiples of π
..., 2π, π, 0, π, 2π, 3π, 4π, ...
Learn more about Least Common Multiple.