Recognised as Number
-3,987
- Negative
- Odd
- 4 digits
-3,987 is an odd 4-digit integer and the negative of 3,987. It has 6 divisors and a digital root of 9.
Number properties
ParityOddnot divisible by 2
SignNegative
Absolute value3,987
Digit count4
Digit sum27
Digit product1,512
Multiplicative persistence3times the digit product can be taken before one digit is left
Digital root9repeated digit sum
PalindromicNoreads differently backwards
Factors & divisors
Prime factorisation−1 × 3^2 × 443
Distinct prime factors23, 443
Number of divisors6
Sum of divisors σ(n)5,772
SquarefreeNohas a repeated prime factor
All divisors1, 3, 9, 443, 1,329, 3,9876 in total
Arithmetic
Previous number-3,988
Next number-3,986
Double-7,974
Half-1,993.5
Square15,896,169
Cube-63,378,025,803
Cube root-15.856795011≈
Negation3,987
Reciprocal-0.0002508151≈
Representations
Decimal-3,987
Binary11111001001112 bits
Octal7623
HexadecimalF93
Base 3632R
In wordsminus three thousand, nine hundred and eighty-seven
Ordinalminus three thousand, nine hundred and eighty-seventh
Scientific notation-3.987 × 10^3
Engineering notation-3.987 × 10^3
In other bases
Ternary12110200base 3; the most digit-efficient integer base after e: 8 digits
Quinary111422base 5; one hand: 6 digits
Septenary14424base 7: 5 digits
Nonary5420base 9; each digit is two ternary digits: 4 digits
Duodecimal2383base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimal9j7base 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal1:6:27base 60; Babylonian, and still how an hour and a circle are divided: 3 digits
Balanced ternaryT11TTT100digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary11000110111101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1111000001101101
Bit length12 bitsto write the magnitude
Set bits8the population count, or Hamming weight
Zero bits4within that length
Bit parityeven8 set bits, so even; not the same as the number itself being odd
Highest set bitbit 11worth 2,048
Lowest set bitbit 00 trailing zeros
Power of twoNo
Bytes20f 93
Gray code100001011010n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1111000001101101two's complement
32-bit11111111111111111111000001101101two's complement
64-bit1111111111111111111111111111111111111111111111111111000001101101two's complement
One's complement0000111110010010at 16 bits, every bit flipped
Bits reversed1011011000001111at 16 bits
Rotated left by 11110000011011011at 16 bits, wrapping
Shifted left by 1-1111100100110= -7,974, no wrap
Shifted right by 1-11111001010= -1,993, discarding the low bit
These bits as a double1.96983973 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-3,987 to the power 215,896,169
-3,987 to the power 3-63,378,025,803
-3,987 to the power 4252,688,188,876,561
-3,987 to the power 5-1,007,467,809,050,848,707
First ten multiples-3,987, -7,974, -11,961, -15,948, -19,935, -23,922, -27,909, -31,896, -35,883, -39,870
Powers of twoBetween 2^11 (2,048) and 2^12 (4,096)
Divisibility tests
Divisible by 2No, remainder 1
Divisible by 3Yes
Divisible by 4No, remainder 3
Divisible by 5No, remainder 2
Divisible by 6No, remainder 3
Divisible by 7No, remainder 4
Divisible by 8No, remainder 3
Divisible by 9Yes
Divisible by 10No, remainder 7
Divisible by 11No, remainder 5
Divisible by 12No, remainder 3
Divisible by 100No, remainder 87
As a percentage & fraction
As a percentage-398,700%
-3,987% as a decimal-39.87
-3,987% of 100-3,987
-3,987% of 1,000-39,870
As a fraction of 100-3,987/100
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