Recognised as Number
-1,072
- Negative
- Even
- 4 digits
-1,072 is an even 4-digit integer and the negative of 1,072. It has 10 divisors and a digital root of 1.
Number properties
ParityEvendivisible by 2
SignNegative
Absolute value1,072
Digit count4
Digit sum10
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root1repeated digit sum
PalindromicNoreads differently backwards
Factors & divisors
Prime factorisation−1 × 2^4 × 67
Distinct prime factors22, 67
Number of divisors10
Sum of divisors σ(n)2,108
SquarefreeNohas a repeated prime factor
All divisors1, 2, 4, 8, 16, 67, 134, 268, 536, 1,07210 in total
Arithmetic
Representations
Decimal-1,072
Binary1000011000011 bits
Octal2060
Hexadecimal430
Base 36TS
In wordsminus one thousand and seventy-two
Ordinalminus one thousand and seventy-second
Scientific notation-1.072 × 10^3
Engineering notation-1.072 × 10^3
In other bases
Ternary1110201base 3; the most digit-efficient integer base after e: 7 digits
Quinary13242base 5; one hand: 5 digits
Septenary3061base 7: 4 digits
Nonary1421base 9; each digit is two ternary digits: 4 digits
Duodecimal754base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 3 digits
Vigesimal2dcbase 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal17:52base 60; Babylonian, and still how an hour and a circle are divided: 2 digits
Balanced ternaryTTTT10Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary110011010000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1111101111010000
Bit length11 bitsto write the magnitude
Set bits3the population count, or Hamming weight
Zero bits8within that length
Bit parityodd3 set bits, so odd; not the same as the number itself being even
Highest set bitbit 10worth 1,024
Lowest set bitbit 44 trailing zeros
Power of twoNo
Bytes204 30
Gray code11000101000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1111101111010000two's complement
32-bit11111111111111111111101111010000two's complement
64-bit1111111111111111111111111111111111111111111111111111101111010000two's complement
One's complement0000010000101111at 16 bits, every bit flipped
Bits reversed0000101111011111at 16 bits
Rotated left by 11111011110100001at 16 bits, wrapping
Shifted left by 1-100001100000= -2,144, no wrap
Shifted right by 1-1000011000= -536, discarding the low bit
These bits as a double5.29638372 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-1,072 to the power 21,149,184
-1,072 to the power 3-1,231,925,248
-1,072 to the power 41,320,623,865,856
-1,072 to the power 5-1,415,708,784,197,632
First ten multiples-1,072, -2,144, -3,216, -4,288, -5,360, -6,432, -7,504, -8,576, -9,648, -10,720
Powers of twoBetween 2^10 (1,024) and 2^11 (2,048)
Divisibility tests
Divisible by 2Yes
Divisible by 3No, remainder 1
Divisible by 4Yes
Divisible by 5No, remainder 2
Divisible by 6No, remainder 4
Divisible by 7No, remainder 1
Divisible by 8Yes
Divisible by 9No, remainder 1
Divisible by 10No, remainder 2
Divisible by 11No, remainder 5
Divisible by 12No, remainder 4
Divisible by 100No, remainder 72
As a percentage & fraction
As a percentage-107,200%
-1,072% as a decimal-10.72
-1,072% of 100-1,072
-1,072% of 1,000-10,720
As a fraction of 100-1,072/100
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