Number reference
121 explained.
121: one hundred twenty-one, composite, perfect square; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred twenty-one
- Classification
- composite
- Factors
- 1, 11, 121
- Prime factorization
- 11 × 11
- Square root
- 11
- Cube root
- 4.946087
- Binary
- 1111001
- Octal
- 171
- Hexadecimal
- 79
- Roman numeral
- CXXI
- Digit sum
- 4
- Digital root
- 4
What makes 121 notable
- Perfect square. 121 = 11², so a square of side 11 has an area of 121.
121 in everyday use
One hundred twenty-one is eleven squared, and it is the smallest palindromic square with more than one digit — 121 reads the same in both directions, and so does the multiplication pattern that produces it: 11 × 11 = 121, 111 × 111 = 12321. In everyday writing "121" is shorthand for one-to-one, as in a 121 meeting. A standard Chinese checkers board has 121 holes, and in Roman numerals the number is CXXI.
It has an unusual second life among factorials: 5! + 1 = 121, making it one of only three known squares of the form n! + 1, alongside 25 and 5,041. Whether any others exist is Brocard's problem, unsolved since 1876. It is also 1 + 3 + 9 + 27 + 81, the sum of the first five powers of three, which means it is written 11111 in base three. Its digit sum is 4, and the digits of 121 read the same forwards and backwards in base ten and in base three alike.
Nearby numbers
How to read this page
The factor list shows every way 121 splits into equal whole-number groups — 3 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 121 for contexts that do not use decimal.
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