26640

26640 is a natural number, positioned between 26639 and 26641. In mathematics it is an even, composite number with a prime factorization of 2^4 × 3^2 × 5 × 37. This factorization shows that 26640 has 60 positive divisors (calculated from (4+1)(2+1)(1+1)(1+1)) and that it is divisible by many common small numbers, including 2, 4, 8, 16, 5, 9, 10, and 40. It can also be expressed as 37 × 720, since 720 = 2^4 × 3^2 × 5.

Other arithmetic properties include that the sum of its divisors is 91,884, and its Euler totient, φ(26640), equals 6,912. The number is a Harshad number in base 10 because the sum of its digits (2+6+6+4+0) equals 18, and 26640 is divisible by 18 (26640/18 = 1,480). It is also a multiple of 120 (26640/120 = 222) and of 40 (26640/40 = 666). In modular arithmetic, 26640 ≡ 5 (mod 7).

These properties make 26640 a useful example in number theory discussions of prime factorization, divisor counts, and totients. Beyond pure math, the number may appear in contexts such as coding examples or computational problems, where its factor structure aids in illustrating divisor-related concepts.