Recognised as Number

31,397

Positive
Odd
Prime
5 digits

31,397 is an odd 5-digit integer and a prime number. It has 2 divisors and a digital root of 5.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value31,397

Digit count5

Digit sum23

Digit product567

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

Digital root5repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation31,397

Distinct prime factors131,397

Number of divisors2

Sum of divisors σ(n)31,398

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)31,396integers below n that share no factor with it

Carmichael function λ(n)31,396the 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, 31,3972 in total

Arithmetic

Previous number31,396

Next number31,398

Double62,794

Half15,698.5

Square985,771,609

Cube30,950,271,207,773

Square root177.191986275≈irrational, shown to 9 decimal places

Cube root31.547337912≈

Negation-31,397

Reciprocal0.0000318502≈

Representations

Decimal31,397

Binary11110101010010115 bits

Octal75245

Hexadecimal7AA5

Base 36O85

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

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

Ordinalthirty-one thousand, three hundred and ninety-seventh

Scientific notation3.1397 × 10^4

Engineering notation31.397 × 10^3

In other bases

Ternary1121001212base 3; the most digit-efficient integer base after e: 10 digits

Quinary2001042base 5; one hand: 7 digits

Septenary160352base 7: 6 digits

Nonary47055base 9; each digit is two ternary digits: 5 digits

Duodecimal16205base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal3i9hbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal8:43:17base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TTT101T0TTdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000111111100101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0111101010100101

Bit length15 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits6within that length

Bit parityodd9 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 a5

Gray code100011111110111n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0111101010100101

32-bit00000000000000000111101010100101

64-bit0000000000000000000000000000000000000000000000000111101010100101

One's complement1000010101011010at 16 bits, every bit flipped

Bits reversed1010010101011110at 16 bits

Rotated left by 11111010101001010at 16 bits, wrapping

Shifted left by 11111010101001010= 62,794, no wrap

Shifted right by 111110101010010= 15,698, discarding the low bit

These bits as a double1.55121791 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime31,469+72

Previous prime31,393−4

Distance to nearest prime0, it is prime

Nearest square below31,329

Nearest square above31,684

Powers & multiples

31,397 to the power 2985,771,609

31,397 to the power 330,950,271,207,773

31,397 to the power 4971,745,665,110,448,881

31,397 to the power 530,509,898,647,472,763,516,757

First ten multiples31,397, 62,794, 94,191, 125,588, 156,985, 188,382, 219,779, 251,176, 282,573, 313,970

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 1

Divisible by 5No, remainder 2

Divisible by 6No, remainder 5

Divisible by 7No, remainder 2

Divisible by 8No, remainder 5

Divisible by 9No, remainder 5

Divisible by 10No, remainder 7

Divisible by 11No, remainder 3

Divisible by 12No, remainder 5

Divisible by 100No, remainder 97

Collatz (3n + 1) trajectory

Steps to reach 1129the total stopping time

Highest value reached381,97612× the starting value

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

First steps31,397 → 94,192 → 47,096 → 23,548 → 11,774 → 5,887 → 17,662 → 8,831 → 26,494 → 13,247 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,139,700%

31,397% as a decimal313.97

31,397% of 10031,397

31,397% of 1,000313,970

As a fraction of 10031,397/100

Read another way

As seconds8 hours, 43 minutes and 17 seconds

As bytes30.661 KiB

As a 24-bit colour#007AA5

Keep nerding

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