Recognised as Number

67,472

Positive
Even
Composite
5 digits

67,472 is an even 5-digit integer and a composite number. It has 10 divisors and a digital root of 8.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value67,472

Digit count5

Digit sum26

Digit product2,352

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

Digital root8repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^4 × 4,217

Distinct prime factors22, 4,217

Number of divisors10

Sum of divisors σ(n)130,758

Aliquot sum63,286sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)33,728integers below n that share no factor with it

Carmichael function λ(n)4,216the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 33,728

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 8, 16, 4,217, 8,434, 16,868, 33,736, 67,47210 in total

Arithmetic

Previous number67,471

Next number67,473

Double134,944

Half33,736

Square4,552,470,784

Cube307,164,308,738,048

Square root259.753729521≈irrational, shown to 9 decimal places

Cube root40.710633567≈

Negation-67,472

Reciprocal0.000014821≈

Representations

Decimal67,472

Binary1000001111001000017 bits

Octal203620

Hexadecimal10790

Base 361G28

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

In wordssixty-seven thousand, four hundred and seventy-two

Ordinalsixty-seven thousand, four hundred and seventy-second

Scientific notation6.7472 × 10^4

Engineering notation67.472 × 10^3

In other bases

Ternary10102112222base 3; the most digit-efficient integer base after e: 11 digits

Quinary4124342base 5; one hand: 7 digits

Septenary400466base 7: 6 digits

Nonary112488base 9; each digit is two ternary digits: 6 digits

Duodecimal33068base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal88dcbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal18:44:32base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary10110TT000Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary10001100010010000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000000010000011110010000

Bit length17 bitsto write the magnitude

Set bits6the population count, or Hamming weight

Zero bits11within that length

Bit parityeven6 set bits, so even; not the same as the number itself being even

Highest set bitbit 16worth 65,536

Lowest set bitbit 44 trailing zeros

Power of twoNo

Bytes301 07 90

Gray code11000010001011000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000000010000011110010000

64-bit0000000000000000000000000000000000000000000000010000011110010000

One's complement11111111111111101111100001101111at 32 bits, every bit flipped

Bits reversed00001001111000001000000000000000at 32 bits

Rotated left by 100000000000000100000111100100000at 32 bits, wrapping

Shifted left by 1100000111100100000= 134,944, no wrap

Shifted right by 11000001111001000= 33,736, discarding the low bit

These bits as a double3.33355973 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime67,477+5

Previous prime67,453−19

Distance to nearest prime5

Nearest square below67,081

Nearest square above67,600

Powers & multiples

67,472 to the power 24,552,470,784

67,472 to the power 3307,164,308,738,048

67,472 to the power 420,724,990,239,173,574,656

67,472 to the power 51,398,356,541,417,519,429,189,632

First ten multiples67,472, 134,944, 202,416, 269,888, 337,360, 404,832, 472,304, 539,776, 607,248, 674,720

Powers of twoBetween 2^16 (65,536) and 2^17 (131,072)

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 2

Divisible by 4Yes

Divisible by 5No, remainder 2

Divisible by 6No, remainder 2

Divisible by 7No, remainder 6

Divisible by 8Yes

Divisible by 9No, remainder 8

Divisible by 10No, remainder 2

Divisible by 11No, remainder 9

Divisible by 12No, remainder 8

Divisible by 100No, remainder 72

Collatz (3n + 1) trajectory

Steps to reach 160the total stopping time

Highest value reached67,472

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

First steps67,472 → 33,736 → 16,868 → 8,434 → 4,217 → 12,652 → 6,326 → 3,163 → 9,490 → 4,745 → …

Last steps… → 32 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage6,747,200%

67,472% as a decimal674.72

67,472% of 10067,472

67,472% of 1,000674,720

As a fraction of 10067,472/100

Read another way

As seconds18 hours, 44 minutes and 32 seconds

As bytes65.891 KiB

As a 24-bit colour#010790

Keep nerding

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