270 (number)
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270 is a natural number lying between 269 and 271. It is a composite number, meaning it has divisors other than 1 and itself. In base ten, it is written with three digits: 2, 7, and 0.
Mathematicians note 270 for its prime factorization: 270 = 2 × 3³ × 5. This decomposition means the number has many divisors relative to its size.
Divisors
270 has 16 positive divisors: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270. Their sum is 720, which can be computed as (1+2) × (1+3+9+27) × (1+5) = 3 × 40 × 6.
Because the sum of proper divisors (all divisors except the number itself) equals 720 − 270 = 450, which is greater than 270, the number is called abundant.
Harmonic divisor number
The harmonic mean of the divisors of 270 is 270 × 16 ÷ 720 = 6, which is a whole number. For this reason, 270 belongs to the harmonic divisor numbers, also known as Ore numbers, a small class of integers studied for their connection to perfect numbers.
Other uses
In geometry, 270 degrees is three-quarters of a rotation, the equivalent of a full rotation (360°) minus 90°. It is also used in navigation and cartography to denote compass bearings, where 270° indicates west.