factor
Something that helps cause a result or outcome.
Factor is something that contributes to a result or helps cause something to happen. When your teacher asks what factors led to the American Revolution, she wants to know all the different things (like unfair taxes, lack of representation, and British troops in colonial towns) that combined to cause the war. If you're trying to figure out why you did poorly on a spelling test, factors might include not studying enough, staying up too late the night before, or feeling sick that morning.
Multiple factors usually work together. Success in school depends on many things working together: factors include effort, good sleep, paying attention, asking questions when confused, and practicing what you learn. When scientists study why forests are healthier in one area than another, they consider factors like rainfall, soil quality, types of trees, and human activity.
In mathematics, a factor means something different: it's a number that divides evenly into another number. The factors of 12 are 1, 2, 3, 4, 6, and 12 because each divides into 12 with no remainder. When you factor a number, you break it down into the numbers that multiply together to make it (like breaking 12 into 3 × 4).