Recognised as Number
-4,008
- Negative
- Even
- 4 digits
-4,008 is an even 4-digit integer and the negative of 4,008. It has 16 divisors and a digital root of 3.
Number properties
ParityEvendivisible by 2
SignNegative
Absolute value4,008
Digit count4
Digit sum12
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root3repeated digit sum
PalindromicNoreads differently backwards
Factors & divisors
Prime factorisation−1 × 2^3 × 3 × 167
Distinct prime factors32, 3, 167
Number of divisors16
Sum of divisors σ(n)10,080
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 6, 8, 12, 24, 167, 334, 501, 668, 1,002, 1,336, 2,004, 4,00816 in total
Arithmetic
Previous number-4,009
Next number-4,007
Double-8,016
Half-2,004
Square16,064,064
Cube-64,384,768,512
Cube root-15.884586146≈
Negation4,008
Reciprocal-0.000249501≈
Representations
Decimal-4,008
Binary11111010100012 bits
Octal7650
HexadecimalFA8
Base 3633C
In wordsminus four thousand and eight
Ordinalminus four thousand and eighth
Scientific notation-4.008 × 10^3
Engineering notation-4.008 × 10^3
In other bases
Ternary12111110base 3; the most digit-efficient integer base after e: 8 digits
Quinary112013base 5; one hand: 6 digits
Septenary14454base 7: 5 digits
Nonary5443base 9; each digit is two ternary digits: 4 digits
Duodecimal23a0base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimala08base 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal1:6:48base 60; Babylonian, and still how an hour and a circle are divided: 3 digits
Balanced ternaryT11TTTTT0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary11000110101000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1111000001011000
Bit length12 bitsto write the magnitude
Set bits7the population count, or Hamming weight
Zero bits5within that length
Bit parityodd7 set bits, so odd; not the same as the number itself being even
Highest set bitbit 11worth 2,048
Lowest set bitbit 33 trailing zeros
Power of twoNo
Bytes20f a8
Gray code100001111100n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1111000001011000two's complement
32-bit11111111111111111111000001011000two's complement
64-bit1111111111111111111111111111111111111111111111111111000001011000two's complement
One's complement0000111110100111at 16 bits, every bit flipped
Bits reversed0001101000001111at 16 bits
Rotated left by 11110000010110001at 16 bits, wrapping
Shifted left by 1-1111101010000= -8,016, no wrap
Shifted right by 1-11111010100= -2,004, discarding the low bit
These bits as a double1.98021511 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-4,008 to the power 216,064,064
-4,008 to the power 3-64,384,768,512
-4,008 to the power 4258,054,152,196,096
-4,008 to the power 5-1,034,281,042,001,952,768
First ten multiples-4,008, -8,016, -12,024, -16,032, -20,040, -24,048, -28,056, -32,064, -36,072, -40,080
Powers of twoBetween 2^11 (2,048) and 2^12 (4,096)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5No, remainder 3
Divisible by 6Yes
Divisible by 7No, remainder 4
Divisible by 8Yes
Divisible by 9No, remainder 3
Divisible by 10No, remainder 8
Divisible by 11No, remainder 4
Divisible by 12Yes
Divisible by 100No, remainder 8
As a percentage & fraction
As a percentage-400,800%
-4,008% as a decimal-40.08
-4,008% of 100-4,008
-4,008% of 1,000-40,080
As a fraction of 100-4,008/100
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