Recognised as Number

13,792

Positive
Even
Composite
5 digits

13,792 is an even 5-digit integer and a composite number. It has 12 divisors and a digital root of 4.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value13,792

Digit count5

Digit sum22

Digit product378

Multiplicative persistence5times the digit product can be taken before one digit is left

Digital root4repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^5 × 431

Distinct prime factors22, 431

Number of divisors12

Sum of divisors σ(n)27,216

Aliquot sum13,424sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)6,880integers below n that share no factor with it

Carmichael function λ(n)1,720the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 6,880

Möbius function μ(n)0zero, because a prime divides n twice

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 8, 16, 32, 431, 862, 1,724, 3,448, 6,896, 13,79212 in total

Arithmetic

Previous number13,791

Next number13,793

Double27,584

Half6,896

Square190,219,264

Cube2,623,504,089,088

Square root117.439346047≈irrational, shown to 9 decimal places

Cube root23.981467174≈

Negation-13,792

Reciprocal0.0000725058≈

Representations

Decimal13,792

Binary1101011110000014 bits

Octal32740

Hexadecimal35E0

Base 36AN4

Roman numeralNot defined above 3,999there is no agreed standard notation

In wordsthirteen thousand, seven hundred and ninety-two

Ordinalthirteen thousand, seven hundred and ninety-second

Scientific notation1.3792 × 10^4

Engineering notation13.792 × 10^3

In other bases

Ternary200220211base 3; the most digit-efficient integer base after e: 9 digits

Quinary420132base 5; one hand: 6 digits

Septenary55132base 7: 5 digits

Nonary20824base 9; each digit is two ternary digits: 5 digits

Duodecimal7b94base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1e9cbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal3:49:52base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T010T1T11digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100101000100000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011010111100000

Bit length14 bitsto write the magnitude

Set bits7the population count, or Hamming weight

Zero bits7within that length

Bit parityodd7 set bits, so odd; not the same as the number itself being even

Highest set bitbit 13worth 8,192

Lowest set bitbit 55 trailing zeros

Power of twoNo

Bytes235 e0

Gray code10111100010000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011010111100000

32-bit00000000000000000011010111100000

64-bit0000000000000000000000000000000000000000000000000011010111100000

One's complement1100101000011111at 16 bits, every bit flipped

Bits reversed0000011110101100at 16 bits

Rotated left by 10110101111000000at 16 bits, wrapping

Shifted left by 1110101111000000= 27,584, no wrap

Shifted right by 11101011110000= 6,896, discarding the low bit

These bits as a double6.81415339 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime13,799+7

Previous prime13,789−3

Distance to nearest prime3

Nearest square below13,689

Nearest square above13,924

Powers & multiples

13,792 to the power 2190,219,264

13,792 to the power 32,623,504,089,088

13,792 to the power 436,183,368,396,701,696

13,792 to the power 5499,041,016,927,309,791,232

First ten multiples13,792, 27,584, 41,376, 55,168, 68,960, 82,752, 96,544, 110,336, 124,128, 137,920

Powers of twoBetween 2^13 (8,192) and 2^14 (16,384)

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 1

Divisible by 4Yes

Divisible by 5No, remainder 2

Divisible by 6No, remainder 4

Divisible by 7No, remainder 2

Divisible by 8Yes

Divisible by 9No, remainder 4

Divisible by 10No, remainder 2

Divisible by 11No, remainder 9

Divisible by 12No, remainder 4

Divisible by 100No, remainder 92

Collatz (3n + 1) trajectory

Steps to reach 145the total stopping time

Highest value reached13,792

Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven

First steps13,792 → 6,896 → 3,448 → 1,724 → 862 → 431 → 1,294 → 647 → 1,942 → 971 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,379,200%

13,792% as a decimal137.92

13,792% of 10013,792

13,792% of 1,000137,920

As a fraction of 10013,792/100

Read another way

As seconds3 hours, 49 minutes and 52 seconds

As bytes13.469 KiB

As a 24-bit colour#0035E0

Keep nerding

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