Live analysis

972,000

972,000 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.).

972,000 (nine hundred seventy-two thousand) is an even 6-digit number. It is a composite number with 144 divisors, and factors as 2⁵ × 3⁵ × 5³. Its proper divisors sum to 2,605,392, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0xED4E0.

Abundant Number Achilles Number Arithmetic Number Evil Number Gapful Number Harshad / Niven Powerful Number Practical Number Refactorable Number Weird Number

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

971,988 971,989 971,990 971,991 971,992 971,993 971,994 971,995 971,996 971,997 971,998 971,999 972,000 972,001 972,002 972,003 972,004 972,005 972,006 972,007 972,008 972,009 972,010 972,011 972,012

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 18
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 20 bits
Reversed: 279
Square (n²): 944,784,000,000
Cube (n³): 918,330,048,000,000,000
Divisor count: 144
σ(n) — sum of divisors: 3,577,392
φ(n) — Euler's totient: 259,200
Sum of prime factors: 40

Primality

Prime factorization: 2 ⁵ × 3 ⁵ × 5 ³

Nearest primes: 971,989 (−11) · 972,001 (+1)

Divisors & multiples

All divisors (144)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 9 · 10 · 12 · 15 · 16 · 18 · 20 · 24 · 25 · 27 · 30 · 32 · 36 · 40 · 45 · 48 · 50 · 54 · 60 · 72 · 75 · 80 · 81 · 90 · 96 · 100 · 108 · 120 · 125 · 135 · 144 · 150 · 160 · 162 · 180 · 200 · 216 · 225 · 240 · 243 · 250 · 270 · 288 · 300 · 324 · 360 · 375 · 400 · 405 · 432 · 450 · 480 · 486 · 500 · 540 · 600 · 648 · 675 · 720 · 750 · 800 · 810 · 864 · 900 · 972 · 1000 · 1080 · 1125 · 1200 · 1215 · 1296 · 1350 · 1440 · 1500 · 1620 · 1800 · 1944 · 2000 · 2025 · 2160 · 2250 · 2400 · 2430 · 2592 · 2700 · 3000 · 3240 · 3375 · 3600 · 3888 · 4000 · 4050 · 4320 · 4500 · 4860 · 5400 · 6000 · 6075 · 6480 · 6750 · 7200 · 7776 · 8100 · 9000 · 9720 · 10125 · 10800 · 12000 · 12150 · 12960 · 13500 · 16200 · 18000 · 19440 · 20250 · 21600 · 24300 · 27000 · 30375 · 32400 · 36000 · 38880 · 40500 · 48600 · 54000 · 60750 · 64800 · 81000 · 97200 · 108000 · 121500 · 162000 · 194400 · 243000 · 324000 · 486000 (half) · 972000

Aliquot sum (sum of proper divisors): 2,605,392

Factor pairs (a × b = 972,000)

1 × 972000

2 × 486000

3 × 324000

4 × 243000

5 × 194400

6 × 162000

8 × 121500

9 × 108000

10 × 97200

12 × 81000

15 × 64800

16 × 60750

18 × 54000

20 × 48600

24 × 40500

25 × 38880

27 × 36000

30 × 32400

32 × 30375

36 × 27000

40 × 24300

45 × 21600

48 × 20250

50 × 19440

54 × 18000

60 × 16200

72 × 13500

75 × 12960

80 × 12150

81 × 12000

90 × 10800

96 × 10125

100 × 9720

108 × 9000

120 × 8100

125 × 7776

135 × 7200

144 × 6750

150 × 6480

160 × 6075

162 × 6000

180 × 5400

200 × 4860

216 × 4500

225 × 4320

240 × 4050

243 × 4000

250 × 3888

270 × 3600

288 × 3375

300 × 3240

324 × 3000

360 × 2700

375 × 2592

400 × 2430

405 × 2400

432 × 2250

450 × 2160

480 × 2025

486 × 2000

500 × 1944

540 × 1800

600 × 1620

648 × 1500

675 × 1440

720 × 1350

750 × 1296

800 × 1215

810 × 1200

864 × 1125

900 × 1080

972 × 1000

First multiples

972,000 · 1,944,000 (double) · 2,916,000 · 3,888,000 · 4,860,000 · 5,832,000 · 6,804,000 · 7,776,000 · 8,748,000 · 9,720,000

Sums & aliquot sequence

As consecutive integers: 323,999 + 324,000 + 324,001 194,398 + 194,399 + 194,400 + 194,401 + 194,402 107,996 + 107,997 + … + 108,004 64,793 + 64,794 + … + 64,807

Aliquot sequence: 972,000 → 2,605,392 → 5,122,288 → 4,802,176 → 4,764,914 → 4,146,382 → 2,101,274 → 1,500,934 → 888,314 → 651,334 → 325,670 → 281,290 → 247,478 → 215,626 → 110,678 → 55,342 → 42,578 — unresolved within range

Continued fraction of √n

√972,000 = [985; (1, 9, 16, 2, 7, 1, 3, 3, 1, 5, 3, 8, 2, 4, 2, 1, 6, 3, 1, 18, 1, 23, 2, 1, …)]

Representations

In words: nine hundred seventy-two thousand
Ordinal: 972000th
Binary: 11101101010011100000
Octal: 3552340
Hexadecimal: 0xED4E0
Base64: DtTg
One's complement: 4,293,995,295 (32-bit)
Scientific notation: 9.72 × 10⁵
As a duration: 972,000 s = 11 days, 6 hours

In other bases

ternary (3) 1211101100000

quaternary (4) 3231103200

quinary (5) 222101000

senary (6) 32500000

septenary (7) 11155551

nonary (9) 1741300

undecimal (11) 604307

duodecimal (12) 3aa600

tridecimal (13) 280563

tetradecimal (14) 1b4328

pentadecimal (15) 143000

As an angle

972,000° = 2,700 × 360°

0° ≈ 0 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹 𒌋𒌋𒌋 · ·
Egyptian hieroglyphic: 𓆐𓆐𓆐𓆐𓆐𓆐𓆐𓆐𓆐𓂍𓂍𓂍𓂍𓂍𓂍𓂍𓆼𓆼
Greek (Milesian): ͵ϡοβ
Chinese: 九十七萬二千
Chinese (financial): 玖拾柒萬貳仟

In other modern scripts

Eastern Arabic ٩٧٢٠٠٠ Devanagari ९७२००० Bengali ৯৭২০০০ Tamil ௯௭௨௦௦௦ Thai ๙๗๒๐๐๐ Tibetan ༩༧༢༠༠༠ Khmer ៩៧២០០០ Lao ໙໗໒໐໐໐ Burmese ၉၇၂၀၀၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 972000, here are decompositions:

11 + 971989 = 972000
19 + 971981 = 972000
23 + 971977 = 972000
41 + 971959 = 972000
61 + 971939 = 972000
67 + 971933 = 972000
79 + 971921 = 972000
83 + 971917 = 972000

Showing the first eight; more decompositions exist.

Hex color

#0ED4E0

RGB(14, 212, 224)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.14.212.224.

Address: 0.14.212.224
Class: reserved
IPv4-mapped IPv6: ::ffff:0.14.212.224

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

Possible US patent number

This number falls in the range of US utility patent numbers. If it's a patent, it would be issued as US 972,000 and was likely granted around 1910.

Patent numbers below 100,000 are excluded as too ambiguous; modern numbering currently reaches roughly 12.5 million.

Look up US972,000 on Google Patents ↗ Look up on USPTO ↗