Recognised as Number

61,672

Positive
Even
Composite
5 digits

61,672 is an even 5-digit integer and a composite number. It has 16 divisors and a digital root of 4.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value61,672

Digit count5

Digit sum22

Digit product504

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

Digital root4repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^3 × 13 × 593

Distinct prime factors32, 13, 593

Number of divisors16

Sum of divisors σ(n)124,740

Aliquot sum63,068sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)28,416integers below n that share no factor with it

Carmichael function λ(n)1,776the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 28,416

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 8, 13, 26, 52, 104, 593, 1,186, 2,372, 4,744, 7,709, 15,418, 30,836, 61,67216 in total

Arithmetic

Previous number61,671

Next number61,673

Double123,344

Half30,836

Square3,803,435,584

Cube234,565,479,336,448

Square root248.338478694≈irrational, shown to 9 decimal places

Cube root39.508997576≈

Negation-61,672

Reciprocal0.0000162148≈

Representations

Decimal61,672

Binary111100001110100016 bits

Octal170350

HexadecimalF0E8

Base 361BL4

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

In wordssixty-one thousand, six hundred and seventy-two

Ordinalsixty-one thousand, six hundred and seventy-second

Scientific notation6.1672 × 10^4

Engineering notation61.672 × 10^3

In other bases

Ternary10010121011base 3; the most digit-efficient integer base after e: 11 digits

Quinary3433142base 5; one hand: 7 digits

Septenary344542base 7: 6 digits

Nonary103534base 9; each digit is two ternary digits: 6 digits

Duodecimal2b834base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal7e3cbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal17:7:52base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary10011TT1011digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary10011000100111000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1111000011101000

Bit length16 bitsto write the magnitude

Set bits8the population count, or Hamming weight

Zero bits8within that length

Bit parityeven8 set bits, so even; not the same as the number itself being even

Highest set bitbit 15worth 32,768

Lowest set bitbit 33 trailing zeros

Power of twoNo

Bytes2f0 e8

Gray code1000100010011100n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1111000011101000

32-bit00000000000000001111000011101000

64-bit0000000000000000000000000000000000000000000000001111000011101000

One's complement0000111100010111at 16 bits, every bit flipped

Bits reversed0001011100001111at 16 bits

Rotated left by 11110000111010001at 16 bits, wrapping

Shifted left by 111110000111010000= 123,344, no wrap

Shifted right by 1111100001110100= 30,836, discarding the low bit

These bits as a double3.04700165 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime61,673+1

Previous prime61,667−5

Distance to nearest prime1

Nearest square below61,504

Nearest square above62,001

Powers & multiples

61,672 to the power 23,803,435,584

61,672 to the power 3234,565,479,336,448

61,672 to the power 414,466,122,241,637,421,056

61,672 to the power 5892,154,690,886,263,031,365,632

First ten multiples61,672, 123,344, 185,016, 246,688, 308,360, 370,032, 431,704, 493,376, 555,048, 616,720

Powers of twoBetween 2^15 (32,768) and 2^16 (65,536)

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 1

Divisible by 4Yes

Divisible by 5No, remainder 2

Divisible by 6No, remainder 4

Divisible by 7No, remainder 2

Divisible by 8Yes

Divisible by 9No, remainder 4

Divisible by 10No, remainder 2

Divisible by 11No, remainder 6

Divisible by 12No, remainder 4

Divisible by 100No, remainder 72

Collatz (3n + 1) trajectory

Steps to reach 155the total stopping time

Highest value reached61,672

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

First steps61,672 → 30,836 → 15,418 → 7,709 → 23,128 → 11,564 → 5,782 → 2,891 → 8,674 → 4,337 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage6,167,200%

61,672% as a decimal616.72

61,672% of 10061,672

61,672% of 1,000616,720

As a fraction of 10061,672/100

Read another way

As seconds17 hours, 7 minutes and 52 seconds

As bytes60.227 KiB

As a 24-bit colour#00F0E8

Keep nerding

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