39

Thirty-nine is the natural number that follows thirty-eight and precedes forty. It is an odd composite number whose prime factorization is 3 × 13, making it a semiprime. The divisors of 39 are 1, 3, 13, and 39, and the sum of its proper divisors is 17, so 39 is a deficient number. Euler’s totient function gives φ(39) = φ(3) · φ(13) = 2 · 12 = 24.

In various numeral systems, 39 is written as XXXIX in Roman numerals, 100111 in binary, 1110 in base 3, and 124 in base 5. The decimal digits add to 12, giving a digital root of 3.

In cultural contexts, the number 39 has appeared in music and literature. Notably, “39” is a song by the British rock band Queen, released in 1975 on the album A Night at the Opera; the track uses a science-fiction theme involving space travel and time dilation.

Geographically and scientifically, the 39th parallel north is a circle of latitude that crosses portions of the northern hemisphere and has appeared in discussions of geography and borders in various regions.

As a mathematical object, 39 is used in number theory examples and puzzles as a product of two primes, a semiprime, and a representative case for studying properties such as divisors, totients, and base representations.