12350

12350 is a natural number that follows 12349 and precedes 12351. In decimal notation it ends with a 0, indicating it is divisible by 10.

Prime factorization and divisors

The prime factorization of 12350 is 2 × 5^2 × 13 × 19. From this factorization, the number has 24 positive divisors. Examples include 1, 2, 5, 10, 25, 50, 13, 26, 65, 130, 325, 650, 19, 38, 95, 190, 475, 950, 247, 494, 1235, 2470, 6175, and 12350. It can also be written as 50 × 247 or 25 × 494.

Representations in other bases

In binary, 12350 is 110000000111110. In octal, it is 30076, and in hexadecimal, it is 0x303E. These alternate representations illustrate how the same value is expressed across numeral systems.

Mathematical properties

Sum of divisors: using the prime factorization, the sum of all divisors is 26040, so the sum of proper divisors is 26040 − 12350 = 13690. Since this exceeds 12350, 12350 is an abundant number, with an abundance of 1340 (13690 − 12350). It is not a sum of two squares, because the prime factor 19 ≡ 3 mod 4 occurs to an odd exponent.

Context

As a composite number with multiple small prime factors, 12350 often appears as a test case in elementary number theory related to divisors, factorization, and base representations.