Recognised as Number

77,141

Positive
Odd
Prime
5 digits

77,141 is an odd 5-digit integer and a prime number. It has 2 divisors and a digital root of 2.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value77,141

Digit count5

Digit sum20

Digit product196

Multiplicative persistence4times the digit product can be taken before one digit is left

Digital root2repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation77,141

Distinct prime factors177,141

Number of divisors2

Sum of divisors σ(n)77,142

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)77,140integers below n that share no factor with it

Carmichael function λ(n)77,140the 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, 77,1412 in total

Arithmetic

Previous number77,140

Next number77,142

Double154,282

Half38,570.5

Square5,950,733,881

Cube459,045,562,314,221

Square root277.742686672≈irrational, shown to 9 decimal places

Cube root42.569160749≈

Negation-77,141

Reciprocal0.0000129633≈

Representations

Decimal77,141

Binary1001011010101010117 bits

Octal226525

Hexadecimal12D55

Base 361NIT

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

In wordsseventy-seven thousand, one hundred and forty-one

Ordinalseventy-seven thousand, one hundred and forty-first

Scientific notation7.7141 × 10^4

Engineering notation77.141 × 10^3

In other bases

Ternary10220211002base 3; the most digit-efficient integer base after e: 11 digits

Quinary4432031base 5; one hand: 7 digits

Septenary440621base 7: 6 digits

Nonary126732base 9; each digit is two ternary digits: 6 digits

Duodecimal38785base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal9ch1base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal21:25:41base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary110T1T1101Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary10111110101010101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000000010010110101010101

Bit length17 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits8within that length

Bit parityodd9 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 16worth 65,536

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes301 2d 55

Gray code11011101111111111n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000000010010110101010101

64-bit0000000000000000000000000000000000000000000000010010110101010101

One's complement11111111111111101101001010101010at 32 bits, every bit flipped

Bits reversed10101010101101001000000000000000at 32 bits

Rotated left by 100000000000000100101101010101010at 32 bits, wrapping

Shifted left by 1100101101010101010= 154,282, no wrap

Shifted right by 11001011010101010= 38,570, discarding the low bit

These bits as a double3.8112718 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime77,153+12

Previous prime77,137−4

Distance to nearest prime0, it is prime

Nearest square below76,729

Nearest square above77,284

Powers & multiples

77,141 to the power 25,950,733,881

77,141 to the power 3459,045,562,314,221

77,141 to the power 435,411,233,722,481,322,161

77,141 to the power 52,731,657,980,585,931,672,821,701

First ten multiples77,141, 154,282, 231,423, 308,564, 385,705, 462,846, 539,987, 617,128, 694,269, 771,410

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 1

Divisible by 5No, remainder 1

Divisible by 6No, remainder 5

Divisible by 7No, remainder 1

Divisible by 8No, remainder 5

Divisible by 9No, remainder 2

Divisible by 10No, remainder 1

Divisible by 11No, remainder 9

Divisible by 12No, remainder 5

Divisible by 100No, remainder 41

Collatz (3n + 1) trajectory

Steps to reach 124the total stopping time

Highest value reached231,4243× the starting value

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

First steps77,141 → 231,424 → 115,712 → 57,856 → 28,928 → 14,464 → 7,232 → 3,616 → 1,808 → 904 → …

Last steps… → 32 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage7,714,100%

77,141% as a decimal771.41

77,141% of 10077,141

77,141% of 1,000771,410

As a fraction of 10077,141/100

Read another way

As seconds21 hours, 25 minutes and 41 seconds

As bytes75.333 KiB

As a 24-bit colour#012D55

Keep nerding

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