7884

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7884 is a natural number that sits between 7883 and 7885. In mathematics, it is an even, composite number with a prime factorization of 2^2 × 3^3 × 73, which means it is divisible by 4, 9, 12, 27, 36, and many other divisors. Equivalently, 7884 = 4 × 27 × 73.

The digits of 7884 sum to 27, so the number is divisible by 9 and by 3. It is also a Harshad number in base 10, since 7884 is divisible by the sum of its digits (27), yielding 292.

Sum of divisors and abundance: the sum of all divisors of 7884 is sigma(7884) = (1+2+4) × (1+3+9+27) × (1+73) = 7 × 40 × 74 = 20,720. Therefore the sum of proper divisors is 20,720 − 7,884 = 12,836, which is greater than 7884. Consequently, 7884 is an abundant number.

Representations in other bases: in binary, 7884 equals 1111011001100_2, and in hexadecimal it is 0x1ECC.

Additional mathematical notes: due to the presence of the prime 3 (which is congruent to 3 mod 4) raised to an odd power in its prime factorization, 7884 cannot be expressed as a sum of two squares. Overall, 7884 is notable for being an abundant, composite Harshad number with prime factors 2, 3, and 73.