31744

31744 is a positive integer. It factors as 31744 = 31 × 1024, so its prime factorization is 2^10 × 31. Since 31 is 2^5 − 1, a Mersenne prime, 31744 can be written as (2^5 − 1) × 2^10.

The number is even and composite. Its 2-adic valuation is 10, meaning the largest power of two dividing it is 2^10 (1024). Consequently, all divisors come in the form 2^k or 2^k × 31 with k = 0, 1, ..., 10, giving a total of 22 positive divisors.

In different bases, 31744 has the representations: binary 0b0111110000000000, hex 0x7C00, and octal 0o76000. This reflects its factorization as a multiple of 1024 and its placement within 16-bit integer ranges (it is less than 2^16).

Other arithmetic properties include a digit sum of 3 + 1 + 7 + 4 + 4 = 19, indicating it is not divisible by 3 or 9. The number is not a perfect square or a prime. Its sum of divisors is σ(31744) = (2^11 − 1) × (31^2 − 1)/(31 − 1) = 2047 × 32 = 65504, which equals 2^16 − 32.