4953

4953 is a natural number that lies between 4952 and 4954. In mathematics, it is a composite, square-free integer with the prime factorization 3 × 13 × 127. Because it is the product of three distinct primes, it has exactly eight positive divisors: 1, 3, 13, 39, 127, 381, 1651, and 4953. The totient of 4953 is 3024, and its sum of divisors is 7168.

In different numeral systems, 4953 is represented as 0x1359 in hexadecimal and 1001101011001 in binary. The digit sum of 4953 is 21, so the number is divisible by 3 but not by 9 (4953 ≡ 3 mod 9). The number is odd and square-free, since no prime factor is repeated.

From a number theory perspective, 4953 cannot be written as a sum of two squares. This follows from Fermat’s theorem on sums of two squares: since 3 and 127 are primes congruent to 3 modulo 4 and appear to the first power in the factorization, no representation as a sum of two squares exists.

Applications and context-wise, 4953 is often cited as an example of a small, square-free composite with eight divisors, illustrating properties of the divisor function, Euler’s totient function, and modular considerations. It serves as a straightforward case in teaching basic factorization and divisor-related concepts.