6048

6048 is a positive integer with several notable mathematical properties. Its prime factorization is 2^5 × 3^3 × 7, showing that it is even and divisible by 3 and 7. With exponents (5, 3, 1), the number has (5+1)(3+1)(1+1) = 48 positive divisors. The sum of all divisors is (2^6−1)/(2−1) × (3^4−1)/(3−1) × (7^2−1)/(7−1) = 63 × 40 × 8 = 20160, so the sum of proper divisors is 14112. Therefore 6048 is an abundant number, with sigma(n)/n = 20160/6048 = 10/3 ≈ 3.33.

6048 is also a Harshad number in base 10 since the sum of its digits is 6+0+4+8 = 18 and 6048/18 = 336. It is a refactorable (tau) number because the divisor-counting function τ(n) = 48 divides 6048 (6048/48 = 126).

In common numeral representations, 6048 equals 0x17A0 in hexadecimal, 0o13640 in octal, and 1011110100000 in binary. The decimal digits sum to 18, giving a digital root of 9. The factorization 2^5 × 3^3 × 7 also expresses 6048 as 32 × 27 × 7. These properties position 6048 as a useful example in the study of divisor structure and numeral representations.