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97920 = 2732517
BaseRepresentation
bin10111111010000000
311222022200
4113322000
511113140
62033200
7555324
oct277200
9158280
1097920
1167629
1248800
1335754
1427984
151e030
hex17e80

97920 has 96 divisors (see below), whose sum is σ = 358020. Its totient is φ = 24576.

The previous prime is 97919. The next prime is 97927. The reversal of 97920 is 2979.

It can be written as a sum of positive squares in 2 ways, for example, as 97344 + 576 = 312^2 + 24^2 .

It is a tau number, because it is divible by the number of its divisors (96).

It is a zygodrome in base 4.

It is not an unprimeable number, because it can be changed into a prime (97927) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 5752 + ... + 5768.

297920 is an apocalyptic number.

97920 is a gapful number since it is divisible by the number (90) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 97920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (179010).

97920 is an abundant number, since it is smaller than the sum of its proper divisors (260100).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

97920 is a wasteful number, since it uses less digits than its factorization.

97920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 42 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 1134, while the sum is 27.

The square root of 97920 is about 312.9217154497. The cubic root of 97920 is about 46.0918141004.

It can be divided in two parts, 979 and 20, that added together give a palindrome (999).

The spelling of 97920 in words is "ninety-seven thousand, nine hundred twenty".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 17 18 20 24 30 32 34 36 40 45 48 51 60 64 68 72 80 85 90 96 102 120 128 136 144 153 160 170 180 192 204 240 255 272 288 306 320 340 360 384 408 480 510 544 576 612 640 680 720 765 816 960 1020 1088 1152 1224 1360 1440 1530 1632 1920 2040 2176 2448 2720 2880 3060 3264 4080 4896 5440 5760 6120 6528 8160 9792 10880 12240 16320 19584 24480 32640 48960 97920