Recognised as Number

45

Positive
Odd
Composite
2 digits

45 is an odd 2-digit integer and a composite number. It has 6 divisors and a digital root of 9.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value45

Digit count2

Digit sum9

Digit product20

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

Digital root9repeated digit sum

PalindromicNoreads differently backwards

Triangular numberYes, the 9th triangular number

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation3^2 × 5

Distinct prime factors23, 5

Number of divisors6

Sum of divisors σ(n)78

Aliquot sum33sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)24integers below n that share no factor with it

Carmichael function λ(n)12the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 24

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

SquarefreeNohas a repeated prime factor

All divisors1, 3, 5, 9, 15, 456 in total

Arithmetic

Previous number44

Next number46

Double90

Half22.5

Square2,025

Cube91,125

Square root6.708203932≈irrational, shown to 9 decimal places

Cube root3.556893304≈

Negation-45

Reciprocal0.0222222222≈

45 factorial119,622,220,865,480,194,561,963,161,495,657,715,064,383,733,760,000,000,000

Representations

Decimal45

Binary1011016 bits

Octal55

Hexadecimal2D

Base 3619

Roman numeralXLV

In wordsforty-five

Ordinalforty-fifth

Scientific notation4.5 × 10^1

Engineering notation45

In other bases

Ternary1200base 3; the most digit-efficient integer base after e: 4 digits

Quinary140base 5; one hand: 3 digits

Septenary63base 7: 2 digits

Nonary50base 9; each digit is two ternary digits: 2 digits

Duodecimal39base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 2 digits

Vigesimal25base 20; hands and feet, and the Mayan and Yoruba systems: 2 digits

Sexagesimal45base 60; Babylonian, and still how an hour and a circle are divided: 1 digit

Balanced ternary1TT00digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary1111101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00101101

Bit length6 bitsto write the magnitude

Set bits4the population count, or Hamming weight

Zero bits2within that length

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

Highest set bitbit 5worth 32

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes12d

Gray code111011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

8-bit00101101

16-bit0000000000101101

32-bit00000000000000000000000000101101

64-bit0000000000000000000000000000000000000000000000000000000000101101

One's complement11010010at 8 bits, every bit flipped

Bits reversed10110100at 8 bits

Rotated left by 101011010at 8 bits, wrapping

Shifted left by 11011010= 90, no wrap

Shifted right by 110110= 22, discarding the low bit

These bits as a double2.22329541 × 10^-322≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime47+2

Previous prime43−2

Distance to nearest prime2

Nearest square below36

Nearest square above49

Powers & multiples

45 to the power 22,025

45 to the power 391,125

45 to the power 44,100,625

45 to the power 5184,528,125

First ten multiples45, 90, 135, 180, 225, 270, 315, 360, 405, 450

Powers of twoBetween 2^5 (32) and 2^6 (64)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3Yes

Divisible by 4No, remainder 1

Divisible by 5Yes

Divisible by 6No, remainder 3

Divisible by 7No, remainder 3

Divisible by 8No, remainder 5

Divisible by 9Yes

Divisible by 10No, remainder 5

Divisible by 11No, remainder 1

Divisible by 12No, remainder 9

Divisible by 100No, remainder 45

Collatz (3n + 1) trajectory

Steps to reach 116the total stopping time

Highest value reached1363× the starting value

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

First steps45 → 136 → 68 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,500%

45% as a decimal0.45

45% of 10045

45% of 1,000450

As a fraction of 10045/100

Read another way

As seconds45 seconds

As bytes45 B

As a 24-bit colour#00002D

Keep nerding

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

45