Recognised as Number

31,357

Positive
Odd
Prime
5 digits

31,357 is an odd 5-digit integer and a prime number. It has 2 divisors and a digital root of 1.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value31,357

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 factorisation31,357

Distinct prime factors131,357

Number of divisors2

Sum of divisors σ(n)31,358

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)31,356integers below n that share no factor with it

Carmichael function λ(n)31,356the smallest exponent with aˣ ≡ 1 for every unit coprime to n

Möbius function μ(n)−11 distinct prime factor, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 31,3572 in total

Arithmetic

Previous number31,356

Next number31,358

Double62,714

Half15,678.5

Square983,261,449

Cube30,832,129,256,293

Square root177.07907838≈irrational, shown to 9 decimal places

Cube root31.533935042≈

Negation-31,357

Reciprocal0.0000318908≈

Representations

Decimal31,357

Binary11110100111110115 bits

Octal75175

Hexadecimal7A7D

Base 36O71

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

In wordsthirty-one thousand, three hundred and fifty-seven

Ordinalthirty-one thousand, three hundred and fifty-seventh

Scientific notation3.1357 × 10^4

Engineering notation31.357 × 10^3

In other bases

Ternary1121000101base 3; the most digit-efficient integer base after e: 10 digits

Quinary2000412base 5; one hand: 7 digits

Septenary160264base 7: 6 digits

Nonary47011base 9; each digit is two ternary digits: 5 digits

Duodecimal16191base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal3i7hbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal8:42:37base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TTT1000101digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000111110001101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0111101001111101

Bit length15 bitsto write the magnitude

Set bits11the population count, or Hamming weight

Zero bits4within that length

Bit parityodd11 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 14worth 16,384

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes27a 7d

Gray code100011101000011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0111101001111101

32-bit00000000000000000111101001111101

64-bit0000000000000000000000000000000000000000000000000111101001111101

One's complement1000010110000010at 16 bits, every bit flipped

Bits reversed1011111001011110at 16 bits

Rotated left by 11111010011111010at 16 bits, wrapping

Shifted left by 11111010011111010= 62,714, no wrap

Shifted right by 111110100111110= 15,678, discarding the low bit

These bits as a double1.54924165 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime31,379+22

Previous prime31,337−20

Distance to nearest prime0, it is prime

Nearest square below31,329

Nearest square above31,684

Powers & multiples

31,357 to the power 2983,261,449

31,357 to the power 330,832,129,256,293

31,357 to the power 4966,803,077,089,579,601

31,357 to the power 530,316,044,088,297,947,548,557

First ten multiples31,357, 62,714, 94,071, 125,428, 156,785, 188,142, 219,499, 250,856, 282,213, 313,570

Powers of twoBetween 2^14 (16,384) and 2^15 (32,768)

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 7No, remainder 4

Divisible by 8No, remainder 5

Divisible by 9No, remainder 1

Divisible by 10No, remainder 7

Divisible by 11No, remainder 7

Divisible by 12No, remainder 1

Divisible by 100No, remainder 57

Collatz (3n + 1) trajectory

Steps to reach 185the total stopping time

Highest value reached200,9326× the starting value

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

First steps31,357 → 94,072 → 47,036 → 23,518 → 11,759 → 35,278 → 17,639 → 52,918 → 26,459 → 79,378 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,135,700%

31,357% as a decimal313.57

31,357% of 10031,357

31,357% of 1,000313,570

As a fraction of 10031,357/100

Read another way

As seconds8 hours, 42 minutes and 37 seconds

As bytes30.622 KiB

As a 24-bit colour#007A7D

Keep nerding

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