Recognised as Number
-1,728
- Negative
- Even
- Perfect cube
- 4 digits
-1,728 is an even 4-digit integer and the negative of 1,728. It has 28 divisors and a digital root of 9.
Number properties
ParityEvendivisible by 2
SignNegative
Absolute value1,728
Digit count4
Digit sum18
Digit product112
Multiplicative persistence2times the digit product can be taken before one digit is left
Digital root9repeated digit sum
PalindromicNoreads differently backwards
Perfect cubeYes, -12³
Factors & divisors
Prime factorisation−1 × 2^6 × 3^3
Distinct prime factors22, 3
Number of divisors28
Sum of divisors σ(n)5,080
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1,72828 in total
Arithmetic
Representations
Decimal-1,728
Binary1101100000011 bits
Octal3300
Hexadecimal6C0
Base 361C0
In wordsminus one thousand, seven hundred and twenty-eight
Ordinalminus one thousand, seven hundred and twenty-eighth
Scientific notation-1.728 × 10^3
Engineering notation-1.728 × 10^3
In other bases
Ternary2101000base 3; the most digit-efficient integer base after e: 7 digits
Quinary23403base 5; one hand: 5 digits
Septenary5016base 7: 4 digits
Nonary2330base 9; each digit is two ternary digits: 4 digits
Duodecimal1000base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimal468base 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal28:48base 60; Babylonian, and still how an hour and a circle are divided: 2 digits
Balanced ternaryT1T0T000digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary100101000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1111100101000000
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 66 trailing zeros
Power of twoNo
Bytes206 c0
Gray code10110100000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1111100101000000two's complement
32-bit11111111111111111111100101000000two's complement
64-bit1111111111111111111111111111111111111111111111111111100101000000two's complement
One's complement0000011010111111at 16 bits, every bit flipped
Bits reversed0000001010011111at 16 bits
Rotated left by 11111001010000001at 16 bits, wrapping
Shifted left by 1-110110000000= -3,456, no wrap
Shifted right by 1-1101100000= -864, discarding the low bit
These bits as a double8.53745436 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-1,728 to the power 22,985,984
-1,728 to the power 3-5,159,780,352
-1,728 to the power 48,916,100,448,256
-1,728 to the power 5-15,407,021,574,586,368
First ten multiples-1,728, -3,456, -5,184, -6,912, -8,640, -10,368, -12,096, -13,824, -15,552, -17,280
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 5No, remainder 3
Divisible by 6Yes
Divisible by 7No, remainder 6
Divisible by 8Yes
Divisible by 9Yes
Divisible by 10No, remainder 8
Divisible by 11No, remainder 1
Divisible by 12Yes
Divisible by 100No, remainder 28
As a percentage & fraction
As a percentage-172,800%
-1,728% as a decimal-17.28
-1,728% of 100-1,728
-1,728% of 1,000-17,280
As a fraction of 100-1,728/100
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