Tim Bowen identifies some important factors in this collection of collocations.

A contributory factor is one that helps to cause something, as in ‘There has been a sharp fall in visitor numbers and the poor weather this summer is widely regarded as a contributory factor’.

Several adjectives collocate with factor to indicate importance, namely critical, crucial, key, major and significant, as well as the word important itself.

A factor that decides something is deciding, decisive or determining, as in ‘Your academic qualifications are important but they may not be the deciding factor in this case’.

A factor that makes something worse is an aggravating factor, as in ‘The fact that excessive violence was used in the robbery is an aggravating factor in this case’.

Something that makes a factor seem less bad is a mitigating factor, as in ‘The court accepted that the medical condition of the accused was a mitigating factor and this was taken into account when sentencing’.

A factor that is basic but not obvious is an underlying factor, as in ‘The survey showed that more than 70% of teachers believed that lack of support from parents was an underlying factor in pupils’ misbehaviour’.

Factors coming from outside a particular situation are external factors, as in ‘External factors, such as the weather, can also have an impact on sales’.

Two nouns are frequently used to collocate with factor, namely risk and lifestyle, as in ‘Untreated high blood pressure has been identified as a risk factor for strokes’ and ‘The increase in the number of cases has been attributed to lifestyle factors such as smoking, drinking alcohol, poor diet and lack of exercise’.