Number reference
34 explained.
34: thirty-four, composite, fibonacci number; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- thirty-four
- Classification
- composite
- Factors
- 1, 2, 17, 34
- Prime factorization
- 2 × 17
- Square root
- 5.830952
- Cube root
- 3.239612
- Binary
- 100010
- Octal
- 42
- Hexadecimal
- 22
- Roman numeral
- XXXIV
- Digit sum
- 7
- Digital root
- 7
What makes 34 notable
- Fibonacci number. 34 appears in the Fibonacci sequence, where each term is the sum of the two before it.
34 in everyday use
Thirty-four is the atomic number of selenium, an element essential in trace amounts and used in photocells. It is the magic constant of the 4 × 4 magic square: every row, column, and diagonal of Albrecht Dürer's square in his 1514 engraving Melencolia I sums to 34, and the bottom row even includes the date. In rugby league and American football 34 is a common jersey number; Walter Payton and Shaquille O'Neal both wore it.
Thirty-four is the ninth Fibonacci number, the sum of 13 and 21, and it factors as 2 × 17. Together with 33 and 35 it forms the first run of three consecutive numbers that all have exactly four divisors. It is the sum of two squares in one way, 9 + 25, and those two squares are themselves the squares of the Fibonacci numbers 3 and 5, an instance of a pattern that runs through the whole sequence. In binary it is 100010, and it has four divisors: 1, 2, 17, and 34.
Nearby numbers
How to read this page
The factor list shows every way 34 splits into equal whole-number groups — 4 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 34 for contexts that do not use decimal.
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