49920 has 72 divisors (see below), whose sum is σ = 171696. Its totient is φ = 12288.

The previous prime is 49919. The next prime is 49921. The reversal of 49920 is 2994.

It is an interprime number because it is at equal distance from previous prime (49919) and next prime (49921).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a nialpdrome in base 16.

It is a zygodrome in base 2.

It is a Saint-Exupery number, since it is equal to the product of the sides of a Pythagorean triangle: 52 × 20 × 48.

It is not an unprimeable number, because it can be changed into a prime (49921) 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, 3834 + ... + 3846.

2^{49920} is an apocalyptic number.

49920 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 49920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (85848).

49920 is an abundant number, since it is smaller than the sum of its proper divisors (121776).

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

49920 is a wasteful number, since it uses less digits than its factorization.

49920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 37 (or 23 counting only the distinct ones).

The product of its (nonzero) digits is 648, while the sum is 24.

The square root of 49920 is about 223.4278407003. The cubic root of 49920 is about 36.8206563301.

49920 divided by its sum of digits (24) gives a triangular number (2080 = T_{64}).

It can be divided in two parts, 49 and 920, that added together give a palindrome (969).

The spelling of 49920 in words is "forty-nine thousand, nine hundred twenty".

Divisors: 1 2 3 4 5 6 8 10 12 13 15 16 20 24 26 30 32 39 40 48 52 60 64 65 78 80 96 104 120 128 130 156 160 192 195 208 240 256 260 312 320 384 390 416 480 520 624 640 768 780 832 960 1040 1248 1280 1560 1664 1920 2080 2496 3120 3328 3840 4160 4992 6240 8320 9984 12480 16640 24960 49920

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