Recognised as Number
-513
- Negative
- Odd
- 3 digits
-513 is an odd 3-digit integer and the negative of 513. It has 8 divisors and a digital root of 9.
Number properties
ParityOddnot divisible by 2
SignNegative
Absolute value513
Digit count3
Digit sum9
Digit product15
Multiplicative persistence2times the digit product can be taken before one digit is left
Digital root9repeated digit sum
PalindromicNoreads differently backwards
Factors & divisors
Prime factorisation−1 × 3^3 × 19
Distinct prime factors23, 19
Number of divisors8
Sum of divisors σ(n)800
SquarefreeNohas a repeated prime factor
All divisors1, 3, 9, 19, 27, 57, 171, 5138 in total
Arithmetic
Representations
Decimal-513
Binary100000000110 bits
Octal1001
Hexadecimal201
Base 36E9
In wordsminus five hundred and thirteen
Ordinalminus five hundred and thirteenth
Scientific notation-5.13 × 10^2
Engineering notation-513
In other bases
Ternary201000base 3; the most digit-efficient integer base after e — 6 digits
Quinary4023base 5; one hand — 4 digits
Septenary1332base 7 — 4 digits
Nonary630base 9; each digit is two ternary digits — 3 digits
Duodecimal369base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves — 3 digits
Vigesimal15dbase 20; hands and feet, and the Mayan and Yoruba systems — 3 digits
Sexagesimal8:33base 60; Babylonian, and still how an hour and a circle are divided — 2 digits
Balanced ternaryT10T000digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1000000011base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1111110111111111
Bit length10 bitsto write the magnitude
Set bits2the population count, or Hamming weight
Zero bits8within that length
Bit parityeven2 set bits, so even; not the same as the number itself being odd
Highest set bitbit 9worth 512
Lowest set bitbit 00 trailing zeros
Power of twoNo
Bytes202 01
Gray code1100000001n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1111110111111111two's complement
32-bit11111111111111111111110111111111two's complement
64-bit1111111111111111111111111111111111111111111111111111110111111111two's complement
One's complement0000001000000000at 16 bits, every bit flipped
Bits reversed1111111110111111at 16 bits
Rotated left by 11111101111111111at 16 bits, wrapping
Shifted left by 1-10000000010= -1,026, no wrap
Shifted right by 1-100000001= -256, discarding the low bit
These bits as a double2.53455676 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-513 to the power 2263,169
-513 to the power 3-135,005,697
-513 to the power 469,257,922,561
-513 to the power 5-35,529,314,273,793
First ten multiples-513, -1,026, -1,539, -2,052, -2,565, -3,078, -3,591, -4,104, -4,617, -5,130
Powers of twoBetween 2^9 (512) and 2^10 (1,024)
Divisibility tests
Divisible by 2No, remainder 1
Divisible by 3Yes
Divisible by 4No, remainder 1
Divisible by 5No, remainder 3
Divisible by 6No, remainder 3
Divisible by 7No, remainder 2
Divisible by 8No, remainder 1
Divisible by 9Yes
Divisible by 10No, remainder 3
Divisible by 11No, remainder 7
Divisible by 12No, remainder 9
Divisible by 100No, remainder 13
As a percentage & fraction
As a percentage-51,300%
-513% as a decimal-5.13
-513% of 100-513
-513% of 1,000-5,130
As a fraction of 100-513/100
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