Number

1,416

1,416 is a composite number, even, a calendar year.

1,416 (one thousand four hundred sixteen) is an even 4-digit number. It is a composite number with 16 divisors, and factors as 2³ × 3 × 59. Its proper divisors sum to 2,184, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MCDXVI and in binary, 10110001000.

Abundant Number Arithmetic Number Evil Number Harshad / Niven Practical Number Recamán's Sequence Semiperfect Number Year Zuckerman Number

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

1,404 1,405 1,406 1,407 1,408 1,409 1,410 1,411 1,412 1,413 1,414 1,415 1,416 1,417 1,418 1,419 1,420 1,421 1,422 1,423 1,424 1,425 1,426 1,427 1,428

less more

Historical context — 1416 AD

Calendar year

Year 1416 (MCDXVI) was a leap year starting on Wednesday of the Julian 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: Monday
January 1, 1416
Ended on: Tuesday
December 31, 1416
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 1410s
1410–1419
Century: 15th century
1401–1500
Millennium: 2nd millennium
1001–2000
Years ago: 610
610 years before 2026.

In other calendars

Hebrew: 5176 / 5177 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 818 / 819 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Fire zodiac:Monkey
Sexagenary cycle position 33 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1959 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 794 / 795 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1408 / 1409 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1338 / 1337 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 12
Digit product: 24
Digital root: 3
Palindrome: No
Bit width: 11 bits
Reversed: 6,141
Recamán's sequence: a(524) = 1,416
Square (n²): 2,005,056
Cube (n³): 2,839,159,296
Divisor count: 16
σ(n) — sum of divisors: 3,600
φ(n) — Euler's totient: 464
Sum of prime factors: 68

Primality

Prime factorization: 2 ³ × 3 × 59

Nearest primes: 1,409 (−7) · 1,423 (+7)

Divisors & multiples

All divisors (16)

1 · 2 · 3 · 4 · 6 · 8 · 12 · 24 · 59 · 118 · 177 · 236 · 354 · 472 · 708 (half) · 1416

Aliquot sum (sum of proper divisors): 2,184

Factor pairs (a × b = 1,416)

1 × 1416

2 × 708

3 × 472

4 × 354

6 × 236

8 × 177

12 × 118

24 × 59

First multiples

1,416 · 2,832 (double) · 4,248 · 5,664 · 7,080 · 8,496 · 9,912 · 11,328 · 12,744 · 14,160

Sums & aliquot sequence

As consecutive integers: 471 + 472 + 473 81 + 82 + … + 96 6 + 7 + … + 53

Aliquot sequence: 1,416 → 2,184 → 4,536 → 9,984 → 18,632 → 18,628 → 13,978 → 7,802 → 4,294 → 2,546 → 1,534 → 986 → 634 → 320 → 442 → 314 → 160 — unresolved within range

Continued fraction of √n

√1,416 = [37; (1, 1, 1, 2, 2, 1, 8, 1, 2, 2, 1, 1, 1, 74)]

Period length 14 — the block in parentheses repeats forever.

Representations

In words: one thousand four hundred sixteen
Ordinal: 1416th
Roman numeral: MCDXVI
Binary: 10110001000
Octal: 2610
Hexadecimal: 0x588
Base64: BYg=
One's complement: 64,119 (16-bit)
Scientific notation: 1.416 × 10³
As a duration: 1,416 s = 23 minutes, 36 seconds

In other bases

ternary (3) 1221110

quaternary (4) 112020

quinary (5) 21131

senary (6) 10320

septenary (7) 4062

nonary (9) 1843

undecimal (11) 1078

duodecimal (12) 9a0

tridecimal (13) 84c

tetradecimal (14) 732

pentadecimal (15) 646

Palindromic in base 15

As an angle

1,416° = 3 × 360° + 336°

336° ≈ 5.864 rad

Compass bearing: NNW (north-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓍢𓍢𓍢𓍢𓎆𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵αυιϛʹ
Mayan (base 20): 𝋣·𝋪·𝋰
Chinese: 一千四百一十六
Chinese (financial): 壹仟肆佰壹拾陸

In other modern scripts

Eastern Arabic ١٤١٦ Devanagari १४१६ Bengali ১৪১৬ Tamil ௧௪௧௬ Thai ๑๔๑๖ Tibetan ༡༤༡༦ Khmer ១៤១៦ Lao ໑໔໑໖ Burmese ၁၄၁၆

Digit at this position in famous constants

π — Pi (π): Digit 1,416 = 0
e — Euler's number (e): Digit 1,416 = 0
φ — Golden ratio (φ): Digit 1,416 = 9
√2 — Pythagoras's (√2): Digit 1,416 = 1
ln 2 — Natural log of 2: Digit 1,416 = 8
γ — Euler-Mascheroni (γ): Digit 1,416 = 6

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1416, here are decompositions:

7 + 1409 = 1416
17 + 1399 = 1416
43 + 1373 = 1416
89 + 1327 = 1416
97 + 1319 = 1416
109 + 1307 = 1416
113 + 1303 = 1416
127 + 1289 = 1416

Showing the first eight; more decompositions exist.

Unicode codepoint

Armenian Small Letter Yi With Stroke

U+0588

Lowercase letter (Ll)

UTF-8 encoding: D6 88 (2 bytes).

Lookup U+0588 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000588

RGB(0, 5, 136)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.5.136.

Address: 0.0.5.136
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.5.136

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

Musical pitch

Heard as a frequency, 1,416 Hz is closest to:

Concert pitch (A4 = 440 Hz): F6 (1396.9 Hz, +23¢)
Scientific pitch (C4 = 256 Hz): F♯6 (1448.2 Hz, -39¢)
Baroque pitch (A4 = 415 Hz): F♯6 (1395.9 Hz, +25¢)

Position in π

The digit sequence 1416 first appears in π at position 3,648 of the decimal expansion (the 3,648ordinal-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 1416 on Pi Search ↗