by a factor of

USAGE SUMMARY

The phrase "by a factor of" is correct and usable in written English.
You can use it to describe how much larger or smaller something is compared to something else, or to describe an increase or decrease by a certain amount. For example: Over the last 10 years, the population of the city has increased by a factor of 2.

✓ Grammatically correct

News & Media

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

We will be smarter by a factor of trillions.

The New York Times

Those odds look mean by a factor of about 10.

The Guardian - Business

"We were wrong by a factor of five".

The New Yorker

Detroit's black population grew by a factor of twenty-four.

The New Yorker

Then the rent went up -- by a factor of ten.

The New York Times

All of a sudden, you're increasing speed not by a factor of ten but by a factor of a hundred, possibly even more".

The New Yorker

Spectrum prices for 4G vary by a factor of 50.

The Economist

It outstrips Washington's White House by a factor of 30.

The Guardian

• INSIDE TRACK: Improved, but not by a factor of 200.

The New York Times

"Participation has increased by a factor of 100 or 200.

The New York Times

The switches exhibit swings in electrical resistance that vary by a factor of 10,000.

The New York Times

Expert writing Tips

Best practice

When using "by a factor of", ensure the context clearly establishes what is being compared. For example, "Sales increased by a factor of three compared to last year."

Common error

Avoid confusing increase with decrease. "Increased by a factor of" means multiplied, while a fractional factor (e.g., 0.5) implies a decrease. Always ensure the numerical factor aligns with the intended direction of change.

Linguistic Context

The phrase "by a factor of" functions as a multiplier or proportional indicator. It specifies the extent to which a quantity has changed relative to its original value, as confirmed by the real-world examples provided by Ludwig.

Expression frequency: Very common

Frequent in

News & Media

65%

Science

30%

Formal & Business

5%

Less common in

Encyclopedias

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, the phrase "by a factor of" serves as a versatile tool for expressing proportional change. As Ludwig AI confirms, it is grammatically sound and frequently employed across various domains, notably in news reporting and scientific writing. When using this phrase, clarity is key: always ensure the context makes the comparison point clear. Common mistakes involve misinterpreting the direction of change or using ambiguous language.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

multiplied by

Focuses on the mathematical operation of multiplication, implying a precise calculation.

increased by

Indicates a general rise or growth without specifying the exact factor.

decreased by

Indicates a general decline or reduction without specifying the exact factor.

times greater than

Emphasizes the magnitude of difference, often used for comparison.

times less than

Emphasizes the magnitude of difference, indicating a reduction or smaller size.

proportionally larger

Highlights the proportional relationship and increase in size.

proportionally smaller

Highlights the proportional relationship and decrease in size.

on the order of

Implies an approximate quantity or scale, less precise than "by a factor of".

in proportion to

Focuses on the proportional relationship between two quantities.

scaled by

Suggests a transformation where values are adjusted based on a multiplier.

FAQs

How do you use "by a factor of" in a sentence?

Use "by a factor of" to indicate how much a quantity has increased or decreased relative to another. For example, "The company's profits increased "by a factor of" two compared to last year".

What's a good alternative to "by a factor of"?

Alternatives include "multiplied by", "increased by", or "times greater than", depending on the specific context.

Is it correct to say "decreased by a factor of 0.5"?

Yes, "decreased by a factor of 0.5" is correct. It means the quantity was halved, or reduced to 50% of its original value. Alternatively, you could say it decreased "by one half".

What's the difference between "increased by a factor of 2" and "increased by 2 times"?

"Increased by a factor of 2" means the quantity doubled (multiplied by 2). "Increased by 2 times" is less precise but generally implies the same meaning. To avoid ambiguity, use "increased by 100 percent" or "doubled" instead of "increased by 2 times".