Recognised as Number
-1,680
- Negative
- Even
- 4 digits
-1,680 is an even 4-digit integer and the negative of 1,680. It has 40 divisors and a digital root of 6.
Number properties
ParityEvendivisible by 2
SignNegative
Absolute value1,680
Digit count4
Digit sum15
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root6repeated digit sum
PalindromicNoreads differently backwards
Factors & divisors
Prime factorisation−1 × 2^4 × 3 × 5 × 7
Distinct prime factors42, 3, 5, 7
Number of divisors40
Sum of divisors σ(n)5,952
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1,68040 in total
Arithmetic
Representations
Decimal-1,680
Binary1101001000011 bits
Octal3220
Hexadecimal690
Base 361AO
In wordsminus one thousand, six hundred and eighty
Ordinalminus one thousand, six hundred and eightieth
Scientific notation-1.68 × 10^3
Engineering notation-1.68 × 10^3
In other bases
Ternary2022020base 3; the most digit-efficient integer base after e: 7 digits
Quinary23210base 5; one hand: 5 digits
Septenary4620base 7: 4 digits
Nonary2266base 9; each digit is two ternary digits: 4 digits
Duodecimalb80base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 3 digits
Vigesimal440base 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal28:0base 60; Babylonian, and still how an hour and a circle are divided: 2 digits
Balanced ternaryT1T01T10digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary111010110000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1111100101110000
Bit length11 bitsto write the magnitude
Set bits4the population count, or Hamming weight
Zero bits7within that length
Bit parityeven4 set bits, so even; not the same as the number itself being even
Highest set bitbit 10worth 1,024
Lowest set bitbit 44 trailing zeros
Power of twoNo
Bytes206 90
Gray code10111011000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1111100101110000two's complement
32-bit11111111111111111111100101110000two's complement
64-bit1111111111111111111111111111111111111111111111111111100101110000two's complement
One's complement0000011010001111at 16 bits, every bit flipped
Bits reversed0000111010011111at 16 bits
Rotated left by 11111001011100001at 16 bits, wrapping
Shifted left by 1-110100100000= -3,360, no wrap
Shifted right by 1-1101001000= -840, discarding the low bit
These bits as a double8.30030285 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-1,680 to the power 22,822,400
-1,680 to the power 3-4,741,632,000
-1,680 to the power 47,965,941,760,000
-1,680 to the power 5-13,382,782,156,800,000
First ten multiples-1,680, -3,360, -5,040, -6,720, -8,400, -10,080, -11,760, -13,440, -15,120, -16,800
Powers of twoBetween 2^10 (1,024) and 2^11 (2,048)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5Yes
Divisible by 6Yes
Divisible by 7Yes
Divisible by 8Yes
Divisible by 9No, remainder 6
Divisible by 10Yes
Divisible by 11No, remainder 8
Divisible by 12Yes
Divisible by 100No, remainder 80
As a percentage & fraction
As a percentage-168,000%
-1,680% as a decimal-16.8
-1,680% of 100-1,680
-1,680% of 1,000-16,800
As a fraction of 100-1,680/100
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