Recognised as Number

15,721

Positive
Odd
Composite
5 digits

15,721 is an odd 5-digit integer and a composite number. It has 4 divisors and a digital root of 7.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value15,721

Digit count5

Digit sum16

Digit product70

Multiplicative persistence2times the digit product can be taken before one digit is left

Digital root7repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation79 × 199

Distinct prime factors279, 199

Number of divisors4

Sum of divisors σ(n)16,000

Aliquot sum279sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)15,444integers below n that share no factor with it

Carmichael function λ(n)2,574the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 15,444

Möbius function μ(n)+12 distinct prime factors, an even number of them

SquarefreeYesno repeated prime factor

All divisors1, 79, 199, 15,7214 in total

Arithmetic

Previous number15,720

Next number15,722

Double31,442

Half7,860.5

Square247,149,841

Cube3,885,442,650,361

Square root125.383411981≈irrational, shown to 9 decimal places

Cube root25.051095499≈

Negation-15,721

Reciprocal0.0000636092≈

Representations

Decimal15,721

Binary1111010110100114 bits

Octal36551

Hexadecimal3D69

Base 36C4P

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

In wordsfifteen thousand, seven hundred and twenty-one

Ordinalfifteen thousand, seven hundred and twenty-first

Scientific notation1.5721 × 10^4

Engineering notation15.721 × 10^3

In other bases

Ternary210120021base 3; the most digit-efficient integer base after e: 9 digits

Quinary1000341base 5; one hand: 7 digits

Septenary63556base 7: 5 digits

Nonary23507base 9; each digit is two ternary digits: 5 digits

Duodecimal9121base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1j61base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal4:22:1base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T11TT01T1digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100001010111001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011110101101001

Bit length14 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits5within that length

Bit parityodd9 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 13worth 8,192

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes23d 69

Gray code10001111011101n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011110101101001

32-bit00000000000000000011110101101001

64-bit0000000000000000000000000000000000000000000000000011110101101001

One's complement1100001010010110at 16 bits, every bit flipped

Bits reversed1001011010111100at 16 bits

Rotated left by 10111101011010010at 16 bits, wrapping

Shifted left by 1111101011010010= 31,442, no wrap

Shifted right by 11111010110100= 7,860, discarding the low bit

These bits as a double7.76720602 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime15,727+6

Previous prime15,683−38

Distance to nearest prime6

Nearest square below15,625

Nearest square above15,876

Powers & multiples

15,721 to the power 2247,149,841

15,721 to the power 33,885,442,650,361

15,721 to the power 461,083,043,906,325,281

15,721 to the power 5960,286,533,251,339,742,601

First ten multiples15,721, 31,442, 47,163, 62,884, 78,605, 94,326, 110,047, 125,768, 141,489, 157,210

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 1

Divisible by 4No, remainder 1

Divisible by 5No, remainder 1

Divisible by 6No, remainder 1

Divisible by 7No, remainder 6

Divisible by 8No, remainder 1

Divisible by 9No, remainder 7

Divisible by 10No, remainder 1

Divisible by 11No, remainder 2

Divisible by 12No, remainder 1

Divisible by 100No, remainder 21

Collatz (3n + 1) trajectory

Steps to reach 184the total stopping time

Highest value reached119,3927× the starting value

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

First steps15,721 → 47,164 → 23,582 → 11,791 → 35,374 → 17,687 → 53,062 → 26,531 → 79,594 → 39,797 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,572,100%

15,721% as a decimal157.21

15,721% of 10015,721

15,721% of 1,000157,210

As a fraction of 10015,721/100

Read another way

As seconds4 hours, 22 minutes and 1 second

As bytes15.353 KiB

As a 24-bit colour#003D69

Keep nerding

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