14421

14421 is a natural number that follows 14420 and precedes 14422. In mathematics, it is notable for its prime factorization: 14421 = 3 × 11 × 19 × 23. The four prime factors are distinct and all congruent to 3 modulo 4, which has implications for its representation as a sum of squares.

As a result of its factorization, 14421 is an odd composite number with exactly 16 positive divisors. The full divisor set is: 1, 3, 11, 19, 23, 33, 57, 69, 209, 253, 437, 627, 759, 1311, 4807, and 14421. It is divisible by 3 and by 11 as well as by other combinations of its prime factors.

Numerical properties include its congruence and square-related observations. 14421 ≡ 1 (mod 4), but because every prime factor of 14421 is congruent to 3 mod 4, it cannot be expressed as a sum of two integer squares. The number is also a multiple of 33 (3 × 11) and 437 (19 × 23).

Euler’s totient function for 14421 can be computed from its prime factors: φ(14421) = 14421 × (1 − 1/3) × (1 − 1/11) × (1 − 1/19) × (1 − 1/23) = 7920. This means there are 7920 integers between 1 and 14420 that are coprime to 14421.

In summary, 14421 is a 5-digit, odd, composite number with a rich factorization structure and several classical number-theory consequences, including its totient value and its non-representability as a sum of two squares.