prime factor

USAGE SUMMARY

"prime factor" is a correct and usable phrase in written English and refers to a number which can only be divided by itself and one.
For example, "Prime factors of 12 are 2 and 6."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

If you can factorize the public key and select the right prime factor, you can decrypt and read the message.

Harvard University

But deforestation was the prime factor.

The New York Times

Kearse is a prime factor.

The New York Times - Sports

The prime factor here is Van Gaal's scattergun management style.

The Guardian - Sport

No. Residency is the prime factor, not nationality or race.

The Guardian

Geography is a prime factor in those traces.

The Washington Post

The order r is some prime factor of q + 1. Write q + 1 = r * h.

Stanford University

The prime factor for selecting equipment is its performance capability and reliability without compromising on quality.

Measurement

Several nesting techniques for the prime factor FFT algorithm are examined.

Journal of Computational Physics

It's anecdotal, but the evidence suggests that the recession is a prime factor.

The New York Times

Pellegrini can now admit De Bruyne's absence was a prime factor that "killed" City's season.

The Guardian - Sport

Expert writing Tips

Best practice

When discussing mathematical concepts, ensure the context clearly defines what number you are factoring and its "prime factor".

Common error

Avoid using "prime factor" when you actually mean 'primary reason' or 'main cause' in non-mathematical contexts. The phrase has a specific mathematical definition, and misusing it can lead to confusion.

Linguistic Context

The phrase "prime factor" functions as a noun, specifically referring to a factor of a given integer that is also a prime number. Examples in Ludwig illustrate its usage in mathematical contexts and in contexts where 'factor' refers to something causally relevant.

Expression frequency: Very common

Frequent in

Science

43%

News & Media

33%

Academia

7%

Less common in

Encyclopedias

3%

Wiki

3%

Formal & Business

0%

Ludwig's WRAP-UP

In summary, "prime factor" is a grammatically sound and frequently used phrase referring to a factor of an integer that is also a prime number. Ludwig AI confirms its usability and provides numerous examples from diverse sources, particularly in scientific, news, and academic contexts. While mainly used in mathematics, it can metaphorically denote a crucial element. When writing, ensure the context justifies its mathematical precision and avoid confusing it with broader causal terms.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

primary factor

Identifies it as the initial or most fundamental.

principal factor

Emphasizes its leading or dominant position.

major factor

Signifies a factor of considerable significance.

prominent factor

Suggests it is easily noticeable and significant.

main factor

Highlights its principal or central role.

premier factor

Indicates the highest-ranking or most important factor.

prime determinant

Emphasizes its role in influencing or deciding an outcome.

prime aspect

Focuses on a particular facet or view that is most important.

prime element

Highlights a fundamental component or ingredient.

prime component

Stresses that the alternative is a constituent part that carries substantial weight.

FAQs

What is the definition of "prime factor"?

A "prime factor" is a factor of a given integer that is also a prime number. For example, the prime factors of 12 are 2 and 3.

How do I use "prime factor" in a sentence?

You can use "prime factor" in sentences such as: 'The order r is some "prime factor" of q + 1', or '2 and 3 are the "prime factors" of 12'.

What's the difference between "prime factor" and "factor"?

A "factor" is any number that divides evenly into another number. A "prime factor" is a factor that is also a prime number (divisible only by 1 and itself).

Can "prime factor" be used outside of mathematics?

While technically a mathematical term, "prime factor" can be metaphorically used to describe a crucial or essential element, similar to "primary factor", though this usage is less common.