Recognised as Number
-32,767
- Negative
- Odd
- 5 digits
-32,767 is an odd 5-digit integer and the negative of 32,767. It has 8 divisors and a digital root of 7.
Number properties
ParityOddnot divisible by 2
SignNegative
Absolute value32,767
Digit count5
Digit sum25
Digit product1,764
Multiplicative persistence5times the digit product can be taken before one digit is left
Digital root7repeated digit sum
PalindromicNoreads differently backwards
Factors & divisors
Prime factorisation−1 × 7 × 31 × 151
Distinct prime factors37, 31, 151
Number of divisors8
Sum of divisors σ(n)38,912
SquarefreeYesno repeated prime factor
All divisors1, 7, 31, 151, 217, 1,057, 4,681, 32,7678 in total
Arithmetic
Representations
Decimal-32,767
Binary11111111111111115 bits
Octal77777
Hexadecimal7FFF
Base 36PA7
In wordsminus thirty-two thousand, seven hundred and sixty-seven
Ordinalminus thirty-two thousand, seven hundred and sixty-seventh
Scientific notation-3.2767 × 10^4
Engineering notation-32.767 × 10^3
In other bases
Ternary1122221121base 3; the most digit-efficient integer base after e: 10 digits
Quinary2022032base 5; one hand: 7 digits
Septenary164350base 7: 6 digits
Nonary48847base 9; each digit is two ternary digits: 5 digits
Duodecimal16b67base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits
Vigesimal41i7base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits
Sexagesimal9:6:7base 60; Babylonian, and still how an hour and a circle are divided: 3 digits
Balanced ternaryT110000111Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1000000000000001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1000000000000001
Bit length15 bitsto write the magnitude
Set bits15the population count, or Hamming weight
Zero bits0within that length
Bit parityodd15 set bits, so odd; not the same as the number itself being odd
Highest set bitbit 14worth 16,384
Lowest set bitbit 00 trailing zeros
Power of twoNo
Bytes27f ff
Gray code100000000000000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1000000000000001two's complement
32-bit11111111111111111000000000000001two's complement
64-bit1111111111111111111111111111111111111111111111111000000000000001two's complement
One's complement0111111111111110at 16 bits, every bit flipped
Bits reversed1000000000000001at 16 bits
Rotated left by 10000000000000011at 16 bits, wrapping
Shifted left by 1-1111111111111110= -65,534, no wrap
Shifted right by 1-100000000000000= -16,383, discarding the low bit
These bits as a double1.6189049 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-32,767 to the power 21,073,676,289
-32,767 to the power 3-35,181,150,961,663
-32,767 to the power 41,152,780,773,560,811,521
-32,767 to the power 5-37,773,167,607,267,111,108,607
First ten multiples-32,767, -65,534, -98,301, -131,068, -163,835, -196,602, -229,369, -262,136, -294,903, -327,670
Powers of twoBetween 2^14 (16,384) and 2^15 (32,768)
Divisibility tests
Divisible by 2No, remainder 1
Divisible by 3No, remainder 1
Divisible by 4No, remainder 3
Divisible by 5No, remainder 2
Divisible by 6No, remainder 1
Divisible by 7Yes
Divisible by 8No, remainder 7
Divisible by 9No, remainder 7
Divisible by 10No, remainder 7
Divisible by 11No, remainder 9
Divisible by 12No, remainder 7
Divisible by 100No, remainder 67
As a percentage & fraction
As a percentage-3,276,700%
-32,767% as a decimal-327.67
-32,767% of 100-32,767
-32,767% of 1,000-327,670
As a fraction of 100-32,767/100
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