Number

48

48 is a composite number, even, a calendar year.

48 (forty-eight) is an even 2-digit number. It is a composite number with 10 divisors, and factors as 2⁴ × 3. Its proper divisors sum to 76, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is XLVIII and in binary, 110000.

Abundant Number Evil Number Harshad / Niven Highly Abundant Highly Composite Number Pernicious Number Practical Number Recamán's Sequence Semiperfect Number Year

Interestingness

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6 notable facts · grade B

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Historical context — 48 AD

Calendar year

AD 48 (XLVIII) was a leap year starting on Monday of the Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Notable events — 48 BC

Aug 9 Caesar defeats Pompey decisively at Pharsalus.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 53
Long year: contains 53 ISO weeks.
Started on: Wednesday
January 1, 48
Ended on: Thursday
December 31, 48
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 40s
40–49
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 1,978
1978 years before 2026.

In other calendars

Hebrew: 3808 / 3809 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Earth zodiac:Monkey
Sexagenary cycle position 45 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 591 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 40 / 41 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -30 / -31 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 2
Digit sum: 12
Digit product: 32
Digital root: 3
Palindrome: No
Bit width: 6 bits
Reversed: 84
Recamán's sequence: a(220) = 48
Square (n²): 2,304
Cube (n³): 110,592
Divisor count: 10
σ(n) — sum of divisors: 124
φ(n) — Euler's totient: 16
Sum of prime factors: 11

Primality

Prime factorization: 2 ⁴ × 3

Nearest primes: 47 (−1) · 53 (+5)

Divisors & multiples

All divisors (10)

1 · 2 · 3 · 4 · 6 · 8 · 12 · 16 · 24 (half) · 48

Aliquot sum (sum of proper divisors): 76

Factor pairs (a × b = 48)

1 × 48

2 × 24

3 × 16

4 × 12

6 × 8

First multiples

48 · 96 (double) · 144 · 192 · 240 · 288 · 336 · 384 · 432 · 480

Sums & aliquot sequence

As consecutive integers: 15 + 16 + 17

Aliquot sequence: 48 → 76 → 64 → 63 → 41 → 1 → 0 — terminates at zero

Continued fraction of √n

√48 = [6; (1, 12)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: forty-eight
Ordinal: 48th
Roman numeral: XLVIII
Binary: 110000
Octal: 60
Hexadecimal: 0x30
Base64: MA==
One's complement: 207 (8-bit)
Scientific notation: 4.8 × 10¹

In other bases

ternary (3) 1210

quaternary (4) 300

quinary (5) 143

senary (6) 120

septenary (7) 66

nonary (9) 53

undecimal (11) 44

duodecimal (12) 40

tridecimal (13) 39

tetradecimal (14) 36

pentadecimal (15) 33

As an angle

48°

48° ≈ 0.838 rad

Compass bearing: NE (northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): μηʹ
Mayan (base 20): 𝋢·𝋨
Chinese: 四十八
Chinese (financial): 肆拾捌

In other modern scripts

Eastern Arabic ٤٨ Devanagari ४८ Bengali ৪৮ Tamil ௪௮ Thai ๔๘ Tibetan ༤༨ Khmer ៤៨ Lao ໔໘ Burmese ၄၈

Digit at this position in famous constants

π — Pi (π): Digit 48 = 7
e — Euler's number (e): Digit 48 = 9
φ — Golden ratio (φ): Digit 48 = 0
√2 — Pythagoras's (√2): Digit 48 = 7
ln 2 — Natural log of 2: Digit 48 = 6
γ — Euler-Mascheroni (γ): Digit 48 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 48, here are decompositions:

5 + 43 = 48
7 + 41 = 48
11 + 37 = 48
17 + 31 = 48
19 + 29 = 48

ASCII character

As an ASCII codepoint, 48 is 0. Printable ASCII character 0.

Hex color

#000030

RGB(0, 0, 48)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.48.

Address: 0.0.0.48
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.48

Unspecified address (0.0.0.0/8) — "this network" placeholder.

Musical pitch

Heard as a frequency, 48 Hz is closest to:

Concert pitch (A4 = 440 Hz): G1 (49 Hz, -36¢)
Scientific pitch (C4 = 256 Hz): G1 (47.9 Hz, +2¢)
Baroque pitch (A4 = 415 Hz): G♯1 (49 Hz, -34¢)

(very low — many laptop and phone speakers can't reproduce it)

As a MIDI note number, 48 is C3 (130.8 Hz at concert pitch).

Atomic number

On the periodic table, atomic number 48 is Cadmium (Cd) — period 5.

Cadmium on Wikipedia ↗