39840

39840 is a natural number that lies between 39839 and 39841. It is an even composite number whose arithmetic properties are commonly used to illustrate divisibility and factorization in number theory.

Its prime factorization is 2^5 × 3 × 5 × 83. This decomposition shows it is divisible by 2, 3, 5, and thus by many of their combinations, such as 6, 10, 15, and 30, among others. Based on the exponents in the factorization, the number has 48 positive divisors (calculated as (5+1)(1+1)(1+1)(1+1)). It also can be expressed as the product 83 × 480, highlighting that 83 is a prime factor.

In different numeral systems, 39840 has multiple compact representations: in hexadecimal it is 0x9BA0, in binary it is 1001101110100000, and in octal it is 0o115640. The digit sum in base 10 is 3+9+8+4+0 = 24, which confirms divisibility by 3. Since the number ends in 0, it is divisible by 2 and 5, and thus by 10, 20, 30, and 480, the latter arising from 32 × 15 or 2^5 × 3 × 5.