Number

972

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

972 (nine hundred seventy-two) is an even 3-digit number. It is a composite number with 18 divisors, and factors as 2² × 3⁵. Its proper divisors sum to 1,576, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is CMLXXII and in binary, 1111001100.

Abundant Number Achilles Number Descending Digits Evil Number Harshad / Niven Powerful Number Practical Number Recamán's Sequence Refactorable Number Semiperfect Number Year

Interestingness

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8 notable facts · grade A

960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984

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Historical context — 972 AD

Calendar year

Year 972 (CMLXXII) 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 →

Historical context — 972 BC

Decade

The 970s BC is a decade that lasted from 979 BC to 970 BC.

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: 53
Long year: contains 53 ISO weeks.
Started on: Wednesday
January 1, 972
Ended on: Thursday
December 31, 972
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 970s
970–979
Century: 10th century
901–1000
Millennium: 1st millennium
1–1000
Years ago: 1,054
1054 years before 2026.

In other calendars

Hebrew: 4732 / 4733 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 361 / 362 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Water zodiac:Monkey
Sexagenary cycle position 9 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1515 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 350 / 351 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 964 / 965 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 894 / 893 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 18
Digit product: 126
Digital root: 9
Palindrome: No
Bit width: 10 bits
Reversed: 279
Recamán's sequence: a(4,475) = 972
Square (n²): 944,784
Cube (n³): 918,330,048
Divisor count: 18
σ(n) — sum of divisors: 2,548
φ(n) — Euler's totient: 324
Sum of prime factors: 19

Primality

Prime factorization: 2 ² × 3 ⁵

Nearest primes: 971 (−1) · 977 (+5)

Divisors & multiples

All divisors (18)

1 · 2 · 3 · 4 · 6 · 9 · 12 · 18 · 27 · 36 · 54 · 81 · 108 · 162 · 243 · 324 · 486 (half) · 972

Aliquot sum (sum of proper divisors): 1,576

Factor pairs (a × b = 972)

1 × 972

2 × 486

3 × 324

4 × 243

6 × 162

9 × 108

12 × 81

18 × 54

27 × 36

First multiples

972 · 1,944 (double) · 2,916 · 3,888 · 4,860 · 5,832 · 6,804 · 7,776 · 8,748 · 9,720

Sums & aliquot sequence

As consecutive integers: 323 + 324 + 325 118 + 119 + … + 125 104 + 105 + … + 112 29 + 30 + … + 52

Aliquot sequence: 972 → 1,576 → 1,394 → 874 → 566 → 286 → 218 → 112 → 136 → 134 → 70 → 74 → 40 → 50 → 43 → 1 → 0 — terminates at zero

Continued fraction of √n

√972 = [31; (5, 1, 1, 1, 7, 6, 1, 3, 1, 14, 1, 3, 1, 6, 7, 1, 1, 1, 5, 62)]

Period length 20 — the block in parentheses repeats forever.

Representations

In words: nine hundred seventy-two
Ordinal: 972nd
Roman numeral: CMLXXII
Binary: 1111001100
Octal: 1714
Hexadecimal: 0x3CC
Base64: A8w=
One's complement: 64,563 (16-bit)
Scientific notation: 9.72 × 10²
As a duration: 972 s = 16 minutes, 12 seconds

In other bases

ternary (3) 1100000

quaternary (4) 33030

quinary (5) 12342

senary (6) 4300

septenary (7) 2556

nonary (9) 1300

undecimal (11) 804

duodecimal (12) 690

tridecimal (13) 59a

tetradecimal (14) 4d6

pentadecimal (15) 44c

As an angle

972° = 2 × 360° + 252°

252° ≈ 4.398 rad

Compass bearing: WSW (west-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺
Greek (Milesian): ϡοβʹ
Mayan (base 20): 𝋢·𝋨·𝋬
Chinese: 九百七十二
Chinese (financial): 玖佰柒拾貳

In other modern scripts

Eastern Arabic ٩٧٢ Devanagari ९७२ Bengali ৯৭২ Tamil ௯௭௨ Thai ๙๗๒ Tibetan ༩༧༢ Khmer ៩៧២ Lao ໙໗໒ Burmese ၉၇၂

Digit at this position in famous constants

π — Pi (π): Digit 972 = 1
e — Euler's number (e): Digit 972 = 8
φ — Golden ratio (φ): Digit 972 = 2
√2 — Pythagoras's (√2): Digit 972 = 4
ln 2 — Natural log of 2: Digit 972 = 0
γ — Euler-Mascheroni (γ): Digit 972 = 9

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 972, here are decompositions:

5 + 967 = 972
19 + 953 = 972
31 + 941 = 972
43 + 929 = 972
53 + 919 = 972
61 + 911 = 972
89 + 883 = 972
109 + 863 = 972

Showing the first eight; more decompositions exist.

Unicode codepoint

Greek Small Letter Omicron With Tonos

U+03CC

Lowercase letter (Ll)

UTF-8 encoding: CF 8C (2 bytes).

Lookup U+03CC on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0003CC

RGB(0, 3, 204)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.204.

Address: 0.0.3.204
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.3.204

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

NANP area code 972

The number 972 is an active NANP area code (North American Numbering Plan).

Primary area: Dallas
Region: Texas
Country: United States

Most NANP area codes have multiple overlays in dense regions; the primary area listed is the historic/largest population center for this code.

Look up area code 972 ↗

Musical pitch

Heard as a frequency, 972 Hz is closest to:

Concert pitch (A4 = 440 Hz): B5 (987.8 Hz, -28¢)
Scientific pitch (C4 = 256 Hz): B5 (966.5 Hz, +10¢)
Baroque pitch (A4 = 415 Hz): C6 (987 Hz, -27¢)