by a factor of

IPA/baɪ ɐ fˈaktəɹ ɒv/
IPA/baɪ ɐ fˈæktɚɹ ʌv/

by a factor of — idiom

1. used before a number to say how many times bigger or smaller something gets, so

1.idiomB2
Definition

used before a number to say how many times bigger or smaller something gets, so the new amount equals the old one multiplied or divided by that number.

Example

After Kasia added the new servers, the website's speed rose by a factor of five.

increase + by a factor of + [number]

The new water filter cut the level of harmful metals by a factor of ten.

decrease + by a factor of + [number]

Common collocations
  • increase by a factor of
  • reduce by a factor of
  • grow by a factor of
  • fall by a factor of
Synonyms
  • times

    plainer everyday wording: 'three times bigger'

  • fold

    suffix form for increases only: 'a threefold rise'

Grammar Patterns

increase/decrease + by a factor of + [number]

Usage Note

Always followed by a specific number that tells you the multiplier; with 'increase' or 'grow' it means times larger, with 'reduce' or 'fall' it means that many times smaller.

Common Mistakes

The cost rose by a factor of 50 percent.
The cost rose by a factor of two.
the number after the phrase is a multiplier, not a percentage.
Output increased in a factor of three.
Output increased by a factor of three.
the fixed preposition is 'by', never 'in'.

Etymology

LatinFrenchEnglish

The phrase joins the everyday preposition 'by' with 'factor', a word taken from mathematics where a factor is a number that divides into another exactly. From the 1800s scientists used 'factor' to mean the number you multiply by, and 'by a factor of' became the standard way to state how many times a quantity grows or shrinks.