Live analysis

3,960

3,960 is a composite number, even.

This number doesn't have a permanent NumberWiki page yet — what you see below is computed live. Pages get added to the permanent index when they're notable (years, primes, curated, etc.).

3,960 (three thousand nine hundred sixty) is an even 4-digit number. It is a composite number with 48 divisors, and factors as 2³ × 3² × 5 × 11. Its proper divisors sum to 10,080, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MMMCMLX and in binary, 111101111000.

Abundant Number Evil Number Gapful Number Harshad / Niven Highly Abundant Practical Number Recamán's Sequence Semiperfect Number

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

3,948 3,949 3,950 3,951 3,952 3,953 3,954 3,955 3,956 3,957 3,958 3,959 3,960 3,961 3,962 3,963 3,964 3,965 3,966 3,967 3,968 3,969 3,970 3,971 3,972

less more

Properties

Parity: Even
Digit count: 4
Digit sum: 18
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 12 bits
Reversed: 693
Recamán's sequence: a(14,471) = 3,960
Square (n²): 15,681,600
Cube (n³): 62,099,136,000
Divisor count: 48
σ(n) — sum of divisors: 14,040
φ(n) — Euler's totient: 960
Sum of prime factors: 28

Primality

Prime factorization: 2 ³ × 3 ² × 5 × 11

Nearest primes: 3,947 (−13) · 3,967 (+7)

Divisors & multiples

All divisors (48)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 9 · 10 · 11 · 12 · 15 · 18 · 20 · 22 · 24 · 30 · 33 · 36 · 40 · 44 · 45 · 55 · 60 · 66 · 72 · 88 · 90 · 99 · 110 · 120 · 132 · 165 · 180 · 198 · 220 · 264 · 330 · 360 · 396 · 440 · 495 · 660 · 792 · 990 · 1320 · 1980 (half) · 3960

Aliquot sum (sum of proper divisors): 10,080

Factor pairs (a × b = 3,960)

1 × 3960

2 × 1980

3 × 1320

4 × 990

5 × 792

6 × 660

8 × 495

9 × 440

10 × 396

11 × 360

12 × 330

15 × 264

18 × 220

20 × 198

22 × 180

24 × 165

30 × 132

33 × 120

36 × 110

40 × 99

44 × 90

45 × 88

55 × 72

60 × 66

First multiples

3,960 · 7,920 (double) · 11,880 · 15,840 · 19,800 · 23,760 · 27,720 · 31,680 · 35,640 · 39,600

Sums & aliquot sequence

As consecutive integers: 1,319 + 1,320 + 1,321 790 + 791 + 792 + 793 + 794 436 + 437 + … + 444 355 + 356 + … + 365

Aliquot sequence: 3,960 → 10,080 → 29,232 → 67,488 → 124,032 → 243,168 → 437,232 → 692,408 → 638,152 → 558,398 → 304,810 → 332,822 → 237,754 → 158,822 → 79,414 → 41,906 → 23,758 — unresolved within range

Continued fraction of √n

√3,960 = [62; (1, 12, 1, 124)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: three thousand nine hundred sixty
Ordinal: 3960th
Roman numeral: MMMCMLX
Binary: 111101111000
Octal: 7570
Hexadecimal: 0xF78
Base64: D3g=
One's complement: 61,575 (16-bit)
Scientific notation: 3.96 × 10³
As a duration: 3,960 s = 1 hour, 6 minutes

In other bases

ternary (3) 12102200

quaternary (4) 331320

quinary (5) 111320

senary (6) 30200

septenary (7) 14355

nonary (9) 5380

undecimal (11) 2a80

duodecimal (12) 2360

tridecimal (13) 1a58

tetradecimal (14) 162c

pentadecimal (15) 1290

As an angle

3,960° = 11 × 360°

0° ≈ 0 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹 𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): ͵γϡξʹ
Mayan (base 20): 𝋩·𝋲·𝋠
Chinese: 三千九百六十
Chinese (financial): 參仟玖佰陸拾

In other modern scripts

Eastern Arabic ٣٩٦٠ Devanagari ३९६० Bengali ৩৯৬০ Tamil ௩௯௬௦ Thai ๓๙๖๐ Tibetan ༣༩༦༠ Khmer ៣៩៦០ Lao ໓໙໖໐ Burmese ၃၉၆၀

Digit at this position in famous constants

π — Pi (π): Digit 3,960 = 1
e — Euler's number (e): Digit 3,960 = 8
φ — Golden ratio (φ): Digit 3,960 = 3
√2 — Pythagoras's (√2): Digit 3,960 = 3
ln 2 — Natural log of 2: Digit 3,960 = 9
γ — Euler-Mascheroni (γ): Digit 3,960 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 3960, here are decompositions:

13 + 3947 = 3960
17 + 3943 = 3960
29 + 3931 = 3960
31 + 3929 = 3960
37 + 3923 = 3960
41 + 3919 = 3960
43 + 3917 = 3960
53 + 3907 = 3960

Showing the first eight; more decompositions exist.

Unicode codepoint

ླྀ

Tibetan Vowel Sign Vocalic L

U+0F78

Non-spacing mark (Mn)

UTF-8 encoding: E0 BD B8 (3 bytes).

Lookup U+0F78 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000F78

RGB(0, 15, 120)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.15.120.

Address: 0.0.15.120
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.15.120

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

Musical pitch

Heard as a frequency, 3,960 Hz is closest to:

Concert pitch (A4 = 440 Hz): B7 (3951.1 Hz, +4¢)
Scientific pitch (C4 = 256 Hz): B7 (3866.1 Hz, +42¢)
Baroque pitch (A4 = 415 Hz): C8 (3948.2 Hz, +5¢)

Position in π

The digit sequence 3960 first appears in π at position 17,946 of the decimal expansion (the 17,946ordinal-suffix:th digit after the integer 3).

Search range: the first 1,000,000 fractional digits of π. Any 6-digit-or-shorter string is virtually guaranteed to appear in there — the more interesting signal is the position.

Look up 3960 on Pi Search ↗