Recognised as Number

15,337

Positive
Odd
Composite
5 digits

15,337 is an odd 5-digit integer and a composite number. It has 6 divisors and a digital root of 1.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value15,337

Digit count5

Digit sum19

Digit product315

Multiplicative persistence3times the digit product can be taken before one digit is left

Digital root1repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation7^2 × 313

Distinct prime factors27, 313

Number of divisors6

Sum of divisors σ(n)17,898

Aliquot sum2,561sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)13,104integers below n that share no factor with it

Carmichael function λ(n)2,184the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 13,104

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

SquarefreeNohas a repeated prime factor

All divisors1, 7, 49, 313, 2,191, 15,3376 in total

Arithmetic

Previous number15,336

Next number15,338

Double30,674

Half7,668.5

Square235,223,569

Cube3,607,623,877,753

Square root123.842642091≈irrational, shown to 9 decimal places

Cube root24.845446498≈

Negation-15,337

Reciprocal0.0000652018≈

Representations

Decimal15,337

Binary1110111110100114 bits

Octal35751

Hexadecimal3BE9

Base 36BU1

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

In wordsfifteen thousand, three hundred and thirty-seven

Ordinalfifteen thousand, three hundred and thirty-seventh

Scientific notation1.5337 × 10^4

Engineering notation15.337 × 10^3

In other bases

Ternary210001001base 3; the most digit-efficient integer base after e: 9 digits

Quinary442322base 5; one hand: 6 digits

Septenary62500base 7: 5 digits

Nonary23031base 9; each digit is two ternary digits: 5 digits

Duodecimal8a61base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1i6hbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal4:15:37base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T10001001digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100110000111001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011101111101001

Bit length14 bitsto write the magnitude

Set bits10the population count, or Hamming weight

Zero bits4within that length

Bit parityeven10 set bits, so even; not the same as the number itself being odd

Highest set bitbit 13worth 8,192

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes23b e9

Gray code10011000011101n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011101111101001

32-bit00000000000000000011101111101001

64-bit0000000000000000000000000000000000000000000000000011101111101001

One's complement1100010000010110at 16 bits, every bit flipped

Bits reversed1001011111011100at 16 bits

Rotated left by 10111011111010010at 16 bits, wrapping

Shifted left by 1111011111010010= 30,674, no wrap

Shifted right by 11110111110100= 7,668, discarding the low bit

These bits as a double7.57748481 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime15,349+12

Previous prime15,331−6

Distance to nearest prime6

Nearest square below15,129

Nearest square above15,376

Powers & multiples

15,337 to the power 2235,223,569

15,337 to the power 33,607,623,877,753

15,337 to the power 455,330,127,413,097,761

15,337 to the power 5848,598,164,134,680,360,457

First ten multiples15,337, 30,674, 46,011, 61,348, 76,685, 92,022, 107,359, 122,696, 138,033, 153,370

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 2

Divisible by 6No, remainder 1

Divisible by 7Yes

Divisible by 8No, remainder 1

Divisible by 9No, remainder 1

Divisible by 10No, remainder 7

Divisible by 11No, remainder 3

Divisible by 12No, remainder 1

Divisible by 100No, remainder 37

Collatz (3n + 1) trajectory

Steps to reach 1239the total stopping time

Highest value reached1,119,47272× the starting value

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

First steps15,337 → 46,012 → 23,006 → 11,503 → 34,510 → 17,255 → 51,766 → 25,883 → 77,650 → 38,825 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,533,700%

15,337% as a decimal153.37

15,337% of 10015,337

15,337% of 1,000153,370

As a fraction of 10015,337/100

Read another way

As seconds4 hours, 15 minutes and 37 seconds

As bytes14.978 KiB

As a 24-bit colour#003BE9

Keep nerding

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