Overview
Seventy (70) is the integer after 69 and before 71. It is an even composite number with three distinct prime factors. In everyday language it is often written as "seventy" and in Roman numerals as LXX. The number appears in many mathematical contexts, in science (atomic number 70) and in cultural expressions.
Mathematical properties
Key arithmetic properties of 70 include:
- Prime factorization: 70 = 2 × 5 × 7.
- Divisors: 1, 2, 5, 7, 10, 14, 35, 70 (eight divisors in total).
- Euler's totient: φ(70) = 24, the count of positive integers less than 70 and coprime to it.
- Sum of divisors: σ(70) = 144 (the proper divisors sum to 74), which makes 70 an abundant number.
- Weird number: 70 is the smallest weird number — it is abundant but cannot be written as a sum of distinct proper divisors.
- Combinatorics: 70 = C(8,4), the number of ways to choose 4 items from 8; it appears in Pascal's triangle.
- Digital and base representations: base-10 digits sum to 7 (so 70 is a Harshad/Niven number), binary 1000110, octal 106, hexadecimal 46.
Occurrences and uses
In chemistry, element 70 is ytterbium (symbol Yb) in the periodic table. In combinatorics and probability, 70 appears as a binomial coefficient and in counting problems. The phrase "three score and ten" has historically been used to denote 70 and is familiar from older English translations of biblical and literary texts.
History and cultural notes
Various cultures and texts highlight the number 70: for example, religious and historical traditions sometimes use 70 in lists or symbolic counts (some New Testament passages refer to seventy or seventy-two disciples in different manuscript traditions). As a round integer, 70 also serves as a milestone age (septuagenarian) and a convenient unit in speech and documentation.
Notable facts
- 70 is the first integer classified as "weird."
- Its full divisor sum, 144, is a perfect square (12²).
- Appears centrally in row 8 of Pascal's triangle as a binomial coefficient.