Number

1,540

1,540 is a composite number, even, a calendar year.

1,540 (one thousand five hundred forty) is an even 4-digit number. It is a composite number with 24 divisors, and factors as 2² × 5 × 7 × 11. Its proper divisors sum to 2,492, more than the number itself, making it an abundant number. It is the 55th triangular number. Written other ways, in Roman numerals it is MDXL and in binary, 11000000100.

Abundant Number Arithmetic Number Cube-Free Decagonal Gapful Number Harshad / Niven Hexagonal Odious Number Pernicious Number Practical Number Recamán's Sequence Semiperfect Number Tetrahedral Triangular Year

Interestingness

★ ★ ★ ★ ★

11 notable facts · grade A

1,528 1,529 1,530 1,531 1,532 1,533 1,534 1,535 1,536 1,537 1,538 1,539 1,540 1,541 1,542 1,543 1,544 1,545 1,546 1,547 1,548 1,549 1,550 1,551 1,552

less more

Notable events — 1540 AD

Sep 27 Pope Paul III formally recognizes the Society of Jesus.
Jul 28 Thomas Cromwell is executed by order of Henry VIII.
Feb 18 Coronado leads an expedition north from Mexico in search of Cíbola.

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: 52
Started on: Monday
January 1, 1540
Ended on: Tuesday
December 31, 1540
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 1540s
1540–1549
Century: 16th century
1501–1600
Millennium: 2nd millennium
1001–2000
Years ago: 486
486 years before 2026.

In other calendars

Hebrew: 5300 / 5301 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 946 / 947 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Rat
Sexagenary cycle position 37 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 2083 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 918 / 919 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1532 / 1533 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1462 / 1461 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 10
Digit product: 0
Digital root: 1
Palindrome: No
Bit width: 11 bits
Reversed: 451
Recamán's sequence: a(1,480) = 1,540
Square (n²): 2,371,600
Cube (n³): 3,652,264,000
Divisor count: 24
σ(n) — sum of divisors: 4,032
φ(n) — Euler's totient: 480
Sum of prime factors: 27

Primality

Prime factorization: 2 ² × 5 × 7 × 11

Nearest primes: 1,531 (−9) · 1,543 (+3)

Divisors & multiples

All divisors (24)

1 · 2 · 4 · 5 · 7 · 10 · 11 · 14 · 20 · 22 · 28 · 35 · 44 · 55 · 70 · 77 · 110 · 140 · 154 · 220 · 308 · 385 · 770 (half) · 1540

Aliquot sum (sum of proper divisors): 2,492

Factor pairs (a × b = 1,540)

1 × 1540

2 × 770

4 × 385

5 × 308

7 × 220

10 × 154

11 × 140

14 × 110

20 × 77

22 × 70

28 × 55

35 × 44

First multiples

1,540 · 3,080 (double) · 4,620 · 6,160 · 7,700 · 9,240 · 10,780 · 12,320 · 13,860 · 15,400

Sums & aliquot sequence

As consecutive integers: 306 + 307 + 308 + 309 + 310 217 + 218 + … + 223 189 + 190 + … + 196 135 + 136 + … + 145

Aliquot sequence: 1,540 → 2,492 → 2,548 → 3,038 → 2,434 → 1,220 → 1,384 → 1,226 → 616 → 824 → 736 → 776 → 694 → 350 → 394 → 200 → 265 — unresolved within range

Continued fraction of √n

√1,540 = [39; (4, 8, 2, 8, 4, 78)]

Period length 6 — the block in parentheses repeats forever.

Representations

In words: one thousand five hundred forty
Ordinal: 1540th
Roman numeral: MDXL
Binary: 11000000100
Octal: 3004
Hexadecimal: 0x604
Base64: BgQ=
One's complement: 63,995 (16-bit)
Scientific notation: 1.54 × 10³
As a duration: 1,540 s = 25 minutes, 40 seconds

In other bases

ternary (3) 2010001

quaternary (4) 120010

quinary (5) 22130

senary (6) 11044

septenary (7) 4330

nonary (9) 2101

undecimal (11) 1180

duodecimal (12) a84

tridecimal (13) 916

tetradecimal (14) 7c0

pentadecimal (15) 6ca

As an angle

1,540° = 4 × 360° + 100°

100° ≈ 1.745 rad

Compass bearing: E (east)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋
Egyptian hieroglyphic: 𓆼𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): ͵αφμʹ
Mayan (base 20): 𝋣·𝋱·𝋠
Chinese: 一千五百四十
Chinese (financial): 壹仟伍佰肆拾

In other modern scripts

Eastern Arabic ١٥٤٠ Devanagari १५४० Bengali ১৫৪০ Tamil ௧௫௪௦ Thai ๑๕๔๐ Tibetan ༡༥༤༠ Khmer ១៥៤០ Lao ໑໕໔໐ Burmese ၁၅၄၀

Digit at this position in famous constants

π — Pi (π): Digit 1,540 = 1
e — Euler's number (e): Digit 1,540 = 5
φ — Golden ratio (φ): Digit 1,540 = 2
√2 — Pythagoras's (√2): Digit 1,540 = 6
ln 2 — Natural log of 2: Digit 1,540 = 8
γ — Euler-Mascheroni (γ): Digit 1,540 = 2

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1540, here are decompositions:

17 + 1523 = 1540
29 + 1511 = 1540
41 + 1499 = 1540
47 + 1493 = 1540
53 + 1487 = 1540
59 + 1481 = 1540
89 + 1451 = 1540
101 + 1439 = 1540

Showing the first eight; more decompositions exist.

Unicode codepoint

Arabic Sign Samvat

U+0604

Format character (Cf)

UTF-8 encoding: D8 84 (2 bytes).

Lookup U+0604 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000604

RGB(0, 6, 4)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.6.4.

Address: 0.0.6.4
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.6.4

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

Musical pitch

Heard as a frequency, 1,540 Hz is closest to:

Concert pitch (A4 = 440 Hz): G6 (1568 Hz, -31¢)
Scientific pitch (C4 = 256 Hz): G6 (1534.3 Hz, +6¢)
Baroque pitch (A4 = 415 Hz): G♯6 (1566.8 Hz, -30¢)

Position in π

The digit sequence 1540 first appears in π at position 21,836 of the decimal expansion (the 21,836ordinal-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 1540 on Pi Search ↗