prime factor

[ prahym fak-ter ]

noun

1. a prime number that is a factor of another number:

   The prime factors of 18 are 2 and 3.

verb (used with or without object)

1. Sometimes prime-factor to resolve (a number) into the prime numbers that are its factors:

   This short video shows how to prime factor a number using a tree diagram.

adjective

1. Sometimes prime-factor relating to or involving prime factors:

   Write out the prime factor expansion for each of the following numbers.

Other Words From

• prime fac·to·rize prime-fac·to·rize verb

Word History and Origins

Origin of prime factor¹

First recorded in 1725–35

Example Sentences

The high cost of living is a prime factor in the ongoing exodus of many Californians, and also may help explain the relatively lackluster mood of people in the state.

From Los Angeles Times

It would happen through a bravura act of mathematics: the separation of some very large numbers, hundreds of digits long, into their prime factors.

From New York Times

As it turns out, interesting band includes about 95.2 percent of all square numbers and 99.7 percent of prime numbers, as well as 39 percent of numbers with many prime factors.

From Scientific American

And now, the "prime factor" causing a bee crisis is climate change caused by global warming, Baysouni said.

From Reuters

“That is the prime factor why it is growing faster and is more resilient than any other luxury — because it’s visceral, deep in our minds and hearts, and global.”

From New York Times