Number reference
101 explained.
101: one hundred one, prime, palindromic prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred one
- Classification
- prime
- Factors
- 1, 101
- Prime factorization
- 101
- Square root
- 10.049876
- Cube root
- 4.65701
- Binary
- 1100101
- Octal
- 145
- Hexadecimal
- 65
- Roman numeral
- CI
- Digit sum
- 2
- Digital root
- 2
What makes 101 notable
- Prime. 101 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
- Palindromic prime. 101 is prime and reads the same forwards and backwards.
101 in everyday use
One hundred one is the number attached to introductory courses. American universities began numbering first-year classes 101 in the early twentieth century, and the label has since escaped the campus: "Cooking 101" or "Investing 101" now means the basics of any subject. The number also names Room 101, the torture chamber in George Orwell's Nineteen Eighty-Four, and the title of Dodie Smith's novel The Hundred and One Dalmatians, later filmed by Disney. In each case the extra one past a round hundred does the work — it signals a first step beyond a threshold.
Mathematically, 101 is the smallest three-digit prime and a palindromic prime, reading the same forwards and backwards. It is the first of a twin-prime pair with 103. Its shape gives it a handy multiplication trick: any two-digit number times 101 is that number written twice, so 47 × 101 = 4747. In binary the digits 101 mean five, a coincidence that programmers sometimes enjoy pointing out.
Nearby numbers
How to read this page
Because 101 is prime, the factor list stops at 1 and 101 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 101 in its prime factorisation inherits it from here.
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