130 (number)

130 is a natural number that comes after 129 and before 131. It is an even number and can be expressed as the product of three distinct prime numbers: 130 = 2 × 5 × 13. For this reason it belongs to the class of numbers known as sphenic, which are numbers composed of exactly three distinct prime factors.

The divisors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130—a total of eight. The sum of all divisors is 252, while the sum of all proper divisors (those less than 130 itself) is 122. Consequently, 130 is a deficient number, since the sum of its proper divisors is less than the number itself.

Mathematical properties

A notable property of 130 is that it equals the sum of the squares of the first four divisors: 1² + 2² + 5² + 10² = 1 + 4 + 25 + 100 = 130. This property is uncommon among natural numbers.

130 can also be expressed as the sum of two perfect squares in two different ways: 130 = 3² + 11² = 9 + 121, and 130 = 7² + 9² = 49 + 81. This capacity is connected to its prime factors—2, 5, and 13—all of which can themselves be expressed as the sum of two perfect squares.

Numeral systems and notation

In Roman numerals, 130 is written as CXXX. In binary (base 2) it is 10000010, and in hexadecimal (base 16) it is 82. In the standard decimal system, 130 consists of three digits: one hundred, three tens, and zero ones.

Other uses

Like other three-digit numbers, 130 appears in measurements, historical dates, population counts, and various numeral systems. In secondary school mathematics, 130 is often used as an example when teaching prime factorization, since its three prime factors are relatively simple.