407 has 4 divisors (see below), whose sum is σ = 456. Its totient is φ = 360.

The previous prime is 401. The next prime is 409. The reversal of 407 is 704.

Adding to 407 its product of nonzero digits (28), we get a triangular number (435 = T_{29}).

Adding to 407 its reverse (704), we get a palindrome (1111).

It is a semiprime because it is the product of two primes, and also a brilliant number, because the two primes have the same length.

It is a cyclic number.

It is not a de Polignac number, because 407 - 2^{8} = 151 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (11), and also a Moran number because the ratio is a prime number: 37 = 407 / (4 + 0 + 7).

It is a magnanimous number.

It is a d-powerful number, because it can be written as **4**^{3} + **0** + **7**^{3} .

It is a pancake number, because a pancake can be divided into 407 parts by 28 straight cuts.

It is a Duffinian number.

407 is an undulating number in base 6.

It is a plaindrome in base 12.

It is a nialpdrome in base 14.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (401) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 8 + ... + 29.

It is an arithmetic number, because the mean of its divisors is an integer number (114).

It is a narcissistic number, because it is equal to **4**^{3} + **0**^{3} + **7**^{3}.

407 is a deficient number, since it is larger than the sum of its proper divisors (49).

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

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

The sum of its prime factors is 48.

The product of its (nonzero) digits is 28, while the sum is 11.

The square root of 407 is about 20.1742410018. The cubic root of 407 is about 7.4107950554.

The spelling of 407 in words is "four hundred seven", and thus it is an aban number and an iban number.

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