45 (number)
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45 is a natural number that lies between 44 and 46. It is an odd number, since it cannot be divided by two, and a composite number because it has divisors other than 1 and itself.
In Roman numerals it is written XLV. In the decimal system, the digits 4 and 5 sum to 9, which means that 45 is divisible by both 9 and 3.
Mathematical properties
The divisors of 45 are 1, 3, 5, 9, 15, and 45. Its prime factorization is 3² × 5. Therefore 45 is the product of 9 and 5, and also of 15 and 3.
45 is a triangular number: it equals the sum of the integers from 1 to 9 (1+2+3+...+9 = 45). It is also among the hexagonal numbers, which form the sequence 1, 6, 15, 28, 45. When 45 is squared, 45² = 2025; if the digits of this result are split and added (20 + 25), the sum is 45, a property known as a Kaprekar number.
Geometric and measurement applications
An angle of 45 degrees is half of a right angle (90 degrees). The 45-degree angle appears consistently in engineering and building diagrams, because it creates equal sides when used to form a right triangle with two equal legs.
Other uses
On the periodic table of chemical elements, atomic number 45 is rhodium (Rh), one of the precious metals. In the Gregorian calendar, 45 denotes the 45th year of any century, for example 1945 and 2045.