102400 has 39 divisors (see below), whose sum is σ = 253921. Its totient is φ = 40960.

The previous prime is 102397. The next prime is 102407. The reversal of 102400 is 4201.

Adding to 102400 its reverse (4201), we get a palindrome (106601).

102400 = T_{319} + T_{320}.

The square root of 102400 is 320.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 36864 + 65536 = 192^2 + 256^2 .

It is a hoax number, since the sum of its digits (7) coincides with the sum of the digits of its distinct prime factors.

It is a Duffinian number.

It is a plaindrome in base 13.

It is a nialpdrome in base 8.

It is not an unprimeable number, because it can be changed into a prime (102407) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 20478 + ... + 20482.

2^{102400} is an apocalyptic number.

102400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

102400 is the 320-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 102400

102400 is an abundant number, since it is smaller than the sum of its proper divisors (151521).

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

102400 is an frugal number, since it uses more digits than its factorization.

102400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 34 (or 7 counting only the distinct ones).

The product of its (nonzero) digits is 8, while the sum is 7.

The cubic root of 102400 is about 46.7842838114.

The spelling of 102400 in words is "one hundred two thousand, four hundred", and thus it is an iban number.

Divisors: 1 2 4 5 8 10 16 20 25 32 40 50 64 80 100 128 160 200 256 320 400 512 640 800 1024 1280 1600 2048 2560 3200 4096 5120 6400 10240 12800 20480 25600 51200 102400

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