90 is the natural number that follows 89 and precedes 91. It is even and composite, and it appears frequently in arithmetic, geometry and everyday counting. In base ten it is written "90" and in Roman numerals as XC. Because 90 = 9 × 10 it is a pronic (or oblong) number, the product of two consecutive integers.
Mathematical properties
The prime factorization of 90 is 2 × 3² × 5. From that factorization one can deduce its divisor count: (1+1)×(2+1)×(1+1) = 12 divisors in total. Its proper divisors sum to 144, which is greater than 90, so 90 is classified as an abundant number.
- Even number and multiple of 10: even
- Prime factorization: 2 × 3² × 5
- Number of divisors: 12
- Pronic (9×10)
Divisors
All positive divisors of 90 are:
Occurrences and uses
One of the most familiar places 90 appears is in geometry: a right angle measures 90 degrees. The number also arises in measurement, calendrical approximations, scores and statistics where round tens are convenient. In number theory and combinatorics 90 serves as a simple example to illustrate factorization, divisor functions and classifications such as abundant or pronic numbers.
Historically and culturally, 90 often marks thresholds (for example, scoring milestones) and is used as a convenient unit because of its many divisors, which allow easy partitioning into equal parts. As a small but composite integer, 90 is a useful teaching example when demonstrating prime factors, divisor sums, and multiplicative functions.