Number reference
72 explained.
72: seventy-two, composite; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- seventy-two
- Classification
- composite
- Factors
- 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Prime factorization
- 2 × 2 × 2 × 3 × 3
- Square root
- 8.485281
- Cube root
- 4.160168
- Binary
- 1001000
- Octal
- 110
- Hexadecimal
- 48
- Roman numeral
- LXXII
- Digit sum
- 9
- Digital root
- 9
What makes 72 notable
- Factor structure. 72 breaks down into 2 distinct primes (2, 3) and has 12 divisors in total, so it can be split into equal whole-number groups 10 ways beyond 1 and itself.
72 in everyday use
Seventy-two points make an inch in typography, so a 72-point letter is nominally an inch tall, and 72 dots per inch was the original Macintosh screen resolution. The rule of 72 estimates how long money takes to double: divide 72 by the interest rate, so 6 percent doubles in about twelve years. Seventy-two is the atomic number of hafnium, used in nuclear control rods. A resting heart beats roughly 72 times a minute, and a pentagon's exterior angles are 72 degrees.
Seventy-two is 2³ × 3² and has twelve divisors. Its most striking property was found by computer in 1966: 72⁵ equals 19⁵ + 43⁵ + 46⁵ + 47⁵ + 67⁵, the first known case of a fifth power that is a sum of five smaller fifth powers. It is the sum of four consecutive primes, 13 + 17 + 19 + 23, and 360 divided by 5 is 72.
Nearby numbers
How to read this page
The factor list shows every way 72 splits into equal whole-number groups — 12 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 72 for contexts that do not use decimal.
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