Number

648

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

648 (six hundred forty-eight) is an even 3-digit number. It is a composite number with 20 divisors, and factors as 2³ × 3⁴. Its proper divisors sum to 1,167, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is DCXLVIII and in binary, 1010001000.

Abundant Number Achilles Number Harshad / Niven Odious Number Pernicious Number Powerful Number Practical Number Recamán's Sequence Self Number Semiperfect Number Smith Number Year

Interestingness

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8 notable facts · grade A

636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660

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Historical context — 648 AD

Calendar year

Year 648 (DCXLVIII) was a leap year starting on Tuesday of the Julian calendar.

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

Historical context — 648 BC

Calendar year

The year 648 BC was a year of the pre-Julian Roman calendar.

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

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 52
Started on: Saturday
January 1, 648
Ended on: Sunday
December 31, 648
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 640s
640–649
Century: 7th century
601–700
Millennium: 1st millennium
1–1000
Years ago: 1,378
1378 years before 2026.

In other calendars

Hebrew: 4408 / 4409 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 27 / 28 AH
Lunar calendar; year spans differ from Gregorian.
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: 1191 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 26 / 27 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 640 / 641 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 570 / 569 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 18
Digit product: 192
Digital root: 9
Palindrome: No
Bit width: 10 bits
Reversed: 846
Recamán's sequence: a(2,328) = 648
Square (n²): 419,904
Cube (n³): 272,097,792
Divisor count: 20
σ(n) — sum of divisors: 1,815
φ(n) — Euler's totient: 216
Sum of prime factors: 18

Primality

Prime factorization: 2 ³ × 3 ⁴

Nearest primes: 647 (−1) · 653 (+5)

Divisors & multiples

All divisors (20)

1 · 2 · 3 · 4 · 6 · 8 · 9 · 12 · 18 · 24 · 27 · 36 · 54 · 72 · 81 · 108 · 162 · 216 · 324 (half) · 648

Aliquot sum (sum of proper divisors): 1,167

Factor pairs (a × b = 648)

1 × 648

2 × 324

3 × 216

4 × 162

6 × 108

8 × 81

9 × 72

12 × 54

18 × 36

24 × 27

First multiples

648 · 1,296 (double) · 1,944 · 2,592 · 3,240 · 3,888 · 4,536 · 5,184 · 5,832 · 6,480

Sums & aliquot sequence

As a sum of two squares: 18² + 18²

As consecutive integers: 215 + 216 + 217 68 + 69 + … + 76 33 + 34 + … + 48 11 + 12 + … + 37

Aliquot sequence: 648 → 1,167 → 393 → 135 → 105 → 87 → 33 → 15 → 9 → 4 → 3 → 1 → 0 — terminates at zero

Continued fraction of √n

√648 = [25; (2, 5, 6, 5, 2, 50)]

Period length 6 — the block in parentheses repeats forever.

Representations

In words: six hundred forty-eight
Ordinal: 648th
Roman numeral: DCXLVIII
Binary: 1010001000
Octal: 1210
Hexadecimal: 0x288
Base64: Aog=
One's complement: 64,887 (16-bit)
Scientific notation: 6.48 × 10²
As a duration: 648 s = 10 minutes, 48 seconds

In other bases

ternary (3) 220000

quaternary (4) 22020

quinary (5) 10043

senary (6) 3000

septenary (7) 1614

nonary (9) 800

undecimal (11) 53a

duodecimal (12) 460

tridecimal (13) 3ab

tetradecimal (14) 344

pentadecimal (15) 2d3

As an angle

648° = 1 × 360° + 288°

288° ≈ 5.027 rad

Compass bearing: WNW (west-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): χμηʹ
Mayan (base 20): 𝋡·𝋬·𝋨
Chinese: 六百四十八
Chinese (financial): 陸佰肆拾捌

In other modern scripts

Eastern Arabic ٦٤٨ Devanagari ६४८ Bengali ৬৪৮ Tamil ௬௪௮ Thai ๖๔๘ Tibetan ༦༤༨ Khmer ៦៤៨ Lao ໖໔໘ Burmese ၆၄၈

Digit at this position in famous constants

π — Pi (π): Digit 648 = 7
e — Euler's number (e): Digit 648 = 0
φ — Golden ratio (φ): Digit 648 = 2
√2 — Pythagoras's (√2): Digit 648 = 9
ln 2 — Natural log of 2: Digit 648 = 6
γ — Euler-Mascheroni (γ): Digit 648 = 1

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 648, here are decompositions:

5 + 643 = 648
7 + 641 = 648
17 + 631 = 648
29 + 619 = 648
31 + 617 = 648
41 + 607 = 648
47 + 601 = 648
61 + 587 = 648

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Small Letter T With Retroflex Hook

U+0288

Lowercase letter (Ll)

UTF-8 encoding: CA 88 (2 bytes).

Lookup U+0288 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000288

RGB(0, 2, 136)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.136.

Address: 0.0.2.136
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.2.136

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

Musical pitch

Heard as a frequency, 648 Hz is closest to:

Concert pitch (A4 = 440 Hz): E5 (659.3 Hz, -30¢)
Scientific pitch (C4 = 256 Hz): E5 (645.1 Hz, +8¢)
Baroque pitch (A4 = 415 Hz): F5 (658.8 Hz, -29¢)