260 (number)
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260 is a natural number in the standard sequence of integers, following 259 and preceding 261. It is an even and composite number, meaning it has divisors other than 1 and itself.
When broken down into prime factors, 260 equals 2 × 2 × 5 × 13, or 2² × 5 × 13. It therefore has 12 divisors: 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, and 260.
Mathematical properties
260 can be expressed as the sum of two squares in two different ways: 16² + 2² = 256 + 4 = 260, and 14² + 8² = 196 + 64 = 260. The capacity of a number to be representable as a sum of two squares in multiple ways depends on its prime factors — in this case 5 and 13, both of which leave remainder 1 when divided by 4.
260 also equals 20 × 13 and 4 × 65. The relationship with 65 is significant in the theory of magic squares, as 65 is the magic constant (the sum of each row, column, and diagonal) of a magic square of order 5.
Magic square of order 8
The formula for the magic constant of a magic square of order n is n(n² + 1)/2. When n = 8, this yields 8 × 65 / 2 = 260. Thus, an 8 × 8 magic square containing the integers 1 through 64 has each row, column, and main diagonal sum to 260. This is also related to the knight's tour on a chessboard when the result forms a semi-magic square.
Other uses
The Tzolk'in calendar system used by Maya civilizations in Mesoamerica consists of 260 days, formed by the combination of 13 and 20. Scholars link the number 260 to the method of counting days with both names and numerals.