Recognised as Number
1
- Positive
- Odd
- Perfect square
- Perfect cube
- 1 digit
1 is an odd 1-digit integer and the multiplicative unit. Its digital root is 1.
Number properties
ParityOddnot divisible by 2
SignPositive
Absolute value1
Digit count1
Digit sum1
Digit product1
Digital root1repeated digit sum
PalindromicYesreads the same backwards
Perfect squareYes, 1²
Perfect cubeYes, 1³
Triangular numberYes, the 1st triangular number
Fibonacci numberYes, F(1)
Happy numberYessquared-digit sums reach 1
Harshad numberYesdivisible by its own digit sum
Armstrong numberYesdigits raised to the digit count sum to itself
Arithmetic
Representations
Decimal1
Binary11 bits
Octal1
Hexadecimal1
Base 361
Roman numeralI
In wordsone
Ordinalfirst
Scientific notation1 × 10^0
Engineering notation1
In other bases
Ternary1base 3; the most digit-efficient integer base after e: 1 digit
Quinary1base 5; one hand: 1 digit
Septenary1base 7: 1 digit
Nonary1base 9; each digit is two ternary digits: 1 digit
Duodecimal1base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 1 digit
Vigesimal1base 20; hands and feet, and the Mayan and Yoruba systems: 1 digit
Sexagesimal1base 60; Babylonian, and still how an hour and a circle are divided: 1 digit
Balanced ternary1digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00000001
Bit length1 bitto write the magnitude
Set bits1the population count, or Hamming weight
Zero bits0within that length
Bit parityodd1 set bits, so odd; not the same as the number itself being odd
Highest set bitbit 0worth 1
Lowest set bitbit 00 trailing zeros
Power of twoYesexactly 2^0, a single set bit
Bytes101
Gray code1n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
8-bit00000001
16-bit0000000000000001
32-bit00000000000000000000000000000001
64-bit0000000000000000000000000000000000000000000000000000000000000001
One's complement11111110at 8 bits, every bit flipped
Bits reversed10000000at 8 bits
Rotated left by 100000010at 8 bits, wrapping
Shifted left by 110= 2, no wrap
Shifted right by 10= 0, discarding the low bit
These bits as a double4.94065646 × 10^-324≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
1 to the power 21
1 to the power 31
1 to the power 41
1 to the power 51
First ten multiples1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Powers of twoExactly 2^0
Divisibility tests
Divisible by 2No, remainder 1
Divisible by 3No, remainder 1
Divisible by 4No, remainder 1
Divisible by 5No, remainder 1
Divisible by 6No, remainder 1
Divisible by 7No, remainder 1
Divisible by 8No, remainder 1
Divisible by 9No, remainder 1
Divisible by 10No, remainder 1
Divisible by 11No, remainder 1
Divisible by 12No, remainder 1
Divisible by 100No, remainder 1
Collatz (3n + 1) trajectory
Steps to reach 10the total stopping time
Highest value reached1
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps1
As a percentage & fraction
As a percentage100%
1% as a decimal0.01
1% of 1001
1% of 1,00010
As a fraction of 1001/100
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Derived from 1
Other readings
Also reads as
U+0031 (unicode character)
- U+0031
- 1
- Decimal digit
U+0031 is code point 49 (1), a decimal digit in the Basic Latin (ASCII) block of the Basic Multilingual Plane. It takes 1 byte in UTF-8 and 1 unit in UTF-16.
Identity
Code pointU+0031
Decimal49
Character1
General categoryDecimal digit
BlockBasic Latin (ASCII)
PlaneBasic Multilingual Planeplane 0
Official nameNot includedthe Unicode Character Database is not bundled; a stale copy would be worse than none
Encodings
UTF-8311 byte
UTF-160031a single unit
UTF-3200000031
Binary110001
Bytes in UTF-8 vs UTF-161 vs 2UTF-16 is not always smaller, even for non-Latin text
Writing it in code
HTML numeric entity1
HTML hex entity1
CSS escape\0031
JavaScript\u0031
Python\u0031
Percent-encoded (URL)%31
Things that catch people out
JavaScript string length1
Needs a surrogate pairNo
Safe in a URL unescapedYes
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