• 424^{2} = 179776 is the smallest square that contains exactly three digits '7'.

• 424 can be written using four 4's:

424 has 8 divisors (see below), whose sum is σ = 810. Its totient is φ = 208.

The previous prime is 421. The next prime is 431.

424 is nontrivially palindromic in base 10.

424 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 324 + 100 = 18^2 + 10^2 .

It is a tau number, because it is divible by the number of its divisors (8).

It is a hoax number, since the sum of its digits (10) coincides with the sum of the digits of its distinct prime factors.

It is a nude number because it is divisible by every one of its digits.

424 is an undulating number in base 10.

It is a plaindrome in base 7, base 11, base 13 and base 14.

It is a nialpdrome in base 8 and base 9.

It is a zygodrome in base 7.

It is a self number, because there is not a number *n* which added to its sum of digits gives 424.

It is not an unprimeable number, because it can be changed into a prime (421) by changing a digit.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 19 + ... + 34.

It is an amenable number.

424 is a deficient number, since it is larger than the sum of its proper divisors (386).

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

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

The sum of its prime factors is 59 (or 55 counting only the distinct ones).

The product of its digits is 32, while the sum is 10.

The square root of 424 is about 20.5912602820. The cubic root of 424 is about 7.5125715084.

Adding to 424 its sum of digits (10), we get a palindrome (434).

Subtracting from 424 its sum of digits (10), we obtain a palindrome (414).

It can be divided in two parts, 4 and 24, that added together give a triangular number (28 = T_{7}).

The spelling of 424 in words is "four hundred twenty-four", and thus it is an aban number and an iban number.

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