Recognised as Number
-840
- Negative
- Even
- 3 digits
-840 is an even 3-digit integer and the negative of 840. It has 32 divisors and a digital root of 3.
Number properties
ParityEvendivisible by 2
SignNegative
Absolute value840
Digit count3
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 × 5 × 7
Distinct prime factors42, 3, 5, 7
Number of divisors32
Sum of divisors σ(n)2,880
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 84032 in total
Arithmetic
Representations
Decimal-840
Binary110100100010 bits
Octal1510
Hexadecimal348
Base 36NC
In wordsminus eight hundred and forty
Ordinalminus eight hundred and fortieth
Scientific notation-8.4 × 10^2
Engineering notation-840
In other bases
Ternary1011010base 3; the most digit-efficient integer base after e: 7 digits
Quinary11330base 5; one hand: 5 digits
Septenary2310base 7: 4 digits
Nonary1133base 9; each digit is two ternary digits: 4 digits
Duodecimal5a0base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 3 digits
Vigesimal220base 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal14:0base 60; Babylonian, and still how an hour and a circle are divided: 2 digits
Balanced ternaryT0TT0T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary110111001000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1111110010111000
Bit length10 bitsto write the magnitude
Set bits4the population count, or Hamming weight
Zero bits6within that length
Bit parityeven4 set bits, so even; not the same as the number itself being even
Highest set bitbit 9worth 512
Lowest set bitbit 33 trailing zeros
Power of twoNo
Bytes203 48
Gray code1011101100n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1111110010111000two's complement
32-bit11111111111111111111110010111000two's complement
64-bit1111111111111111111111111111111111111111111111111111110010111000two's complement
One's complement0000001101000111at 16 bits, every bit flipped
Bits reversed0001110100111111at 16 bits
Rotated left by 11111100101110001at 16 bits, wrapping
Shifted left by 1-11010010000= -1,680, no wrap
Shifted right by 1-110100100= -420, discarding the low bit
These bits as a double4.15015143 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-840 to the power 2705,600
-840 to the power 3-592,704,000
-840 to the power 4497,871,360,000
-840 to the power 5-418,211,942,400,000
First ten multiples-840, -1,680, -2,520, -3,360, -4,200, -5,040, -5,880, -6,720, -7,560, -8,400
Powers of twoBetween 2^9 (512) and 2^10 (1,024)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5Yes
Divisible by 6Yes
Divisible by 7Yes
Divisible by 8Yes
Divisible by 9No, remainder 3
Divisible by 10Yes
Divisible by 11No, remainder 4
Divisible by 12Yes
Divisible by 100No, remainder 40
As a percentage & fraction
As a percentage-84,000%
-840% as a decimal-8.4
-840% of 100-840
-840% of 1,000-8,400
As a fraction of 100-840/100
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