# Smooth number

## Integer having only small prime factors / From Wikipedia, the free encyclopedia

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In number theory, an ** n-smooth** (or

**)**

*n*-friable**number**is an integer whose prime factors are all less than or equal to

*n*.

^{[1]}

^{[2]}For example, a 7-smooth number is a number in which every prime factor is at most 7. Therefore, 49 = 7

^{2}and 15750 = 2 × 3

^{2}× 5

^{3}× 7 are both 7-smooth, while 11 and 702 = 2 × 3

^{3}× 13 are not 7-smooth. The term seems to have been coined by Leonard Adleman.

^{[3]}Smooth numbers are especially important in cryptography, which relies on factorization of integers. 2-smooth numbers are simply the powers of 2, while 5-smooth numbers are also known as regular numbers.