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420 = 22357

420 has 24 divisors (see below), whose sum is σ = 1344. Its totient is φ = 96.

The previous prime is 419. The next prime is 421. The reversal of 420 is 24.

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

It is an interprime number because it is at equal distance from previous prime (419) and next prime (421).

It is a Harshad number since it is a multiple of its sum of digits (6).

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

It is a O'Halloran number.

It is a straight-line number, since its digits are in arithmetic progression.

It is a nialpdrome in base 8, base 10 and base 14.

It is a junction number, because it is equal to n+sod(n) for n = 399 and 408.

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 in 7 ways as a sum of consecutive naturals, for example, 57 + ... + 63.

It is an arithmetic number, because the mean of its divisors is an integer number (56).

It is a pronic number, being equal to 20×21.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 420, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (672).

420 is an abundant number, since it is smaller than the sum of its proper divisors (924).

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

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

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

The sum of its prime factors is 19 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 8, while the sum is 6.

The square root of 420 is about 20.4939015319. The cubic root of 420 is about 7.4888723872.

The spelling of 420 in words is "four hundred twenty", and is thus an aban number and an iban number.

Divisors: 1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35 42 60 70 84 105 140 210 420