Number reference
3 explained.
3: three, prime, mersenne prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- three
- Classification
- prime
- Factors
- 1, 3
- Prime factorization
- 3
- Square root
- 1.732051
- Cube root
- 1.44225
- Binary
- 11
- Octal
- 3
- Hexadecimal
- 3
- Roman numeral
- III
- Digit sum
- 3
- Digital root
- 3
What makes 3 notable
- Prime. 3 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
- Mersenne prime. 3 = 2^2 − 1 and is prime, making it a Mersenne prime. These are the primes that large prime searches concentrate on.
3 in everyday use
Three is the atomic number of lithium, the lightest metal and the workhorse of rechargeable batteries. Space has three dimensions, a triangle has three sides, and the stable stool has three legs because any three points define a plane. In sport a hat-trick is three goals or wickets, and in photography the rule of thirds splits a frame into a three-by-three grid. Stories run on threes too: three acts, three wishes, three little pigs — the smallest count that establishes a pattern.
Three is the second prime and the first odd one, and it is the second triangular number, since one plus two makes three. It is a Fermat prime (2¹ + 1), which is why a regular triangle can be drawn with compass and straightedge. Its best-known trick is the divisibility test: add a number's digits, and if the total divides by 3 so does the number, because 10 leaves a remainder of 1 when divided by 3.
Nearby numbers
How to read this page
Because 3 is prime, the factor list stops at 1 and 3 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 3 in its prime factorisation inherits it from here.
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