Number reference

4 explained.

4: four, composite, power of two; factors, prime factorization, roots, binary, hexadecimal, and digit properties.

Identity and representations

Written form
four
Classification
composite
Factors
1, 2, 4
Prime factorization
2 × 2
Square root
2
Cube root
1.587401
Binary
100
Octal
4
Hexadecimal
4
Roman numeral
IV
Digit sum
4
Digital root
4

What makes 4 notable

4 in everyday use

Four is the atomic number of beryllium and the number of seasons, cardinal directions, and suits in a deck of cards. Quarters divide the year, the hour, the football game, and the dollar. In Mandarin, Cantonese, Japanese, and Korean the word for four sounds close to the word for death, so many buildings in East Asia skip a fourth floor much as Western buildings skip a thirteenth. The four-leaf clover owes its reputation to rarity: roughly one clover in five thousand has an extra leaf.

Four is the smallest composite number and the first square above one, being 2 × 2. Lagrange proved in 1770 that every whole number is the sum of at most four squares, so 7 needs all four (4 + 1 + 1 + 1) but nothing ever needs five. The four-colour theorem, settled by computer in 1976, says any flat map can be coloured with four colours so no two neighbouring regions match. A number divides by 4 whenever its last two digits do.

Nearby numbers

How to read this page

The factor list shows every way 4 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 4 for contexts that do not use decimal.

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