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100400400 = 2432521672
BaseRepresentation
bin1011111101111…
…11110100010000
320222220212110100
411332333310100
5201200303100
613543532400
72326250352
oct576776420
9228825410
10100400400
1151745341
122975a100
1317a53b29
14d4970d2
158c33400
hex5fbfd10

100400400 has 135 divisors (see below), whose sum is σ = 350516101. Its totient is φ = 26613120.

The previous prime is 100400393. The next prime is 100400437. The reversal of 100400400 is 4004001.

The square root of 100400400 is 10020.

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., 36144144 + 64256256 = 6012^2 + 8016^2 .

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 601117 + ... + 601283.

Almost surely, 2100400400 is an apocalyptic number.

100400400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

100400400 is the 10020-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 100400400

100400400 is an abundant number, since it is smaller than the sum of its proper divisors (250115701).

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

100400400 is a wasteful number, since it uses less digits than its factorization.

100400400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 358 (or 177 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 9.

The cubic root of 100400400 is about 464.7775557627. Note that the first 3 decimals are identical.

Multiplying 100400400 by its product of nonzero digits (16), we get a square (1606406400 = 400802).

100400400 divided by its product of nonzero digits (16) gives a square (6275025 = 25052).

Adding to 100400400 its reverse (4004001), we get a palindrome (104404401).

Multiplying 100400400 by its reverse (4004001), we get a square (402003302000400 = 200500202).

The spelling of 100400400 in words is "one hundred million, four hundred thousand, four hundred".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 36 40 45 48 50 60 72 75 80 90 100 120 144 150 167 180 200 225 240 300 334 360 400 450 501 600 668 720 835 900 1002 1200 1336 1503 1670 1800 2004 2505 2672 3006 3340 3600 4008 4175 5010 6012 6680 7515 8016 8350 10020 12024 12525 13360 15030 16700 20040 24048 25050 27889 30060 33400 37575 40080 50100 55778 60120 66800 75150 83667 100200 111556 120240 139445 150300 167334 200400 223112 251001 278890 300600 334668 418335 446224 502002 557780 601200 669336 697225 836670 1004004 1115560 1255005 1338672 1394450 1673340 2008008 2091675 2231120 2510010 2788900 3346680 4016016 4183350 5020020 5577800 6275025 6693360 8366700 10040040 11155600 12550050 16733400 20080080 25100100 33466800 50200200 100400400