52 (number)
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52 is a natural number that falls between 51 and 53. It is an even number, as it is divisible by two with no remainder. In Roman numerals it is written as LII.
52 is a composite number, meaning it has divisors other than 1 and itself. Its divisors are 1, 2, 4, 13, 26, and 52.
Mathematical properties
The prime factorization of 52 is 2 × 2 × 13, also written as 2² × 13. The sum of its proper divisors—1, 2, 4, 13, and 26—is 46, which is less than 52. For this reason 52 is classified as a deficient number, one whose proper divisors sum to less than the number itself.
52 is also described as an untouchable number, meaning it is not the sum of the proper divisors of any other natural number. These represent a rare class of numbers studied in number theory.
Common use
The Gregorian calendar year contains 52 complete weeks, plus additional days. For this reason 52 is regularly used in work planning, manufacturing, and annual accounting—for example, weekly pay or weekly reports.
A standard deck of playing cards contains 52 cards, divided into four suits with 13 cards each. This reflects the same factorization of 4 × 13.