Recognised as Number

75

Positive
Odd
Composite
2 digits

75 is an odd 2-digit integer and a composite number. It has 6 divisors and a digital root of 3.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value75

Digit count2

Digit sum12

Digit product35

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

Digital root3repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation3 × 5^2

Distinct prime factors23, 5

Number of divisors6

Sum of divisors σ(n)124

Aliquot sum49sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)40integers below n that share no factor with it

Carmichael function λ(n)20the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 40

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

SquarefreeNohas a repeated prime factor

All divisors1, 3, 5, 15, 25, 756 in total

Arithmetic

Previous number74

Next number76

Double150

Half37.5

Square5,625

Cube421,875

Square root8.660254038≈irrational, shown to 9 decimal places

Cube root4.217163327≈

Negation-75

Reciprocal0.0133333333≈

75 factorial2480914081139539809194647711659403366092… (110 digits)

Representations

Decimal75

Binary10010117 bits

Octal113

Hexadecimal4B

Base 3623

Roman numeralLXXV

In wordsseventy-five

Ordinalseventy-fifth

Scientific notation7.5 × 10^1

Engineering notation75

In other bases

Ternary2210base 3; the most digit-efficient integer base after e: 4 digits

Quinary300base 5; one hand: 3 digits

Septenary135base 7: 3 digits

Nonary83base 9; each digit is two ternary digits: 2 digits

Duodecimal63base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 2 digits

Vigesimal3fbase 20; hands and feet, and the Mayan and Yoruba systems: 2 digits

Sexagesimal1:15base 60; Babylonian, and still how an hour and a circle are divided: 2 digits

Balanced ternary10T10digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary1011111base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

01001011

Bit length7 bitsto write the magnitude

Set bits4the population count, or Hamming weight

Zero bits3within that length

Bit parityeven4 set bits, so even; not the same as the number itself being odd

Highest set bitbit 6worth 64

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes14b

Gray code1101110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

8-bit01001011

16-bit0000000001001011

32-bit00000000000000000000000001001011

64-bit0000000000000000000000000000000000000000000000000000000001001011

One's complement10110100at 8 bits, every bit flipped

Bits reversed11010010at 8 bits

Rotated left by 110010110at 8 bits, wrapping

Shifted left by 110010110= 150, no wrap

Shifted right by 1100101= 37, discarding the low bit

These bits as a double3.70549234 × 10^-322≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime79+4

Previous prime73−2

Distance to nearest prime2

Nearest square below64

Nearest square above81

Powers & multiples

75 to the power 25,625

75 to the power 3421,875

75 to the power 431,640,625

75 to the power 52,373,046,875

First ten multiples75, 150, 225, 300, 375, 450, 525, 600, 675, 750

Powers of twoBetween 2^6 (64) and 2^7 (128)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3Yes

Divisible by 4No, remainder 3

Divisible by 5Yes

Divisible by 6No, remainder 3

Divisible by 7No, remainder 5

Divisible by 8No, remainder 3

Divisible by 9No, remainder 3

Divisible by 10No, remainder 5

Divisible by 11No, remainder 9

Divisible by 12No, remainder 3

Divisible by 100No, remainder 75

Collatz (3n + 1) trajectory

Steps to reach 114the total stopping time

Highest value reached3404× the starting value

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

First steps75 → 226 → 113 → 340 → 170 → 85 → 256 → 128 → 64 → 32 → …

Last steps… → 32 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage7,500%

75% as a decimal0.75

75% of 10075

75% of 1,000750

As a fraction of 10075/100

Read another way

As seconds1 minute and 15 seconds

As bytes75 B

As a 24-bit colour#00004B

Keep nerding

Every link below is a page Nerdulator can generate from what it already knows about this value.

75