96 (number)

"Number 96" redirects here. For the Australian soap opera, see Number 96 (TV series). For the 1974 drama film, see Number 96 (film).

96 (ninety-six) is the natural number following 95 and preceding 97. It is a number that appears the same when rotated by 180 degrees.

← 95 96 97 →
← 90 91 92 93 94 95 96 97 98 99 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	ninety-six
Ordinal	96th (ninety-sixth)
Factorization	25 × 3
Divisors	1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Greek numeral	ϞϚ´
Roman numeral	XCVI, xcvi
Binary	11000002
Ternary	101203
Senary	2406
Octal	1408
Duodecimal	8012
Hexadecimal	6016

In mathematics

96 as the difference of two squares (in orange).

96 is:

• an octagonal number.^[1]
• a refactorable number.^[2]
• an untouchable number.^[3]
• a semiperfect number since it is a multiple of 6.
• an abundant number since the sum of its proper divisors is greater than 96.
• the fourth Granville number and the second non-perfect Granville number. The next Granville number is 126, the previous being 24.
• the sum of Euler's totient function φ(x) over the first seventeen integers.
• strobogrammatic in bases 10 (96₁₀), 11 (88₁₁) and 95 (11₉₅).
• palindromic in bases 11 (88₁₁), 15 (66₁₅), 23 (44₂₃), 31 (33₃₁), 47 (22₄₇) and 95 (11₉₅).
• an Erdős–Woods number, since it is possible to find sequences of 96 consecutive integers such that each inner member shares a factor with either the first or the last member.^[4]
• divisible by the number of prime numbers (24) below 96.
• the smallest natural number that can be expressed as the difference of two nonzero squares in more than three ways: ${\displaystyle 10^{2}-2^{2}}$, ${\displaystyle 11^{2}-5^{2}}$, ${\displaystyle 14^{2}-10^{2}}$ or ${\displaystyle 25^{2}-23^{2}}$.^[5]

The number of divisors of 96 is 12.^[6] As no smaller number has more than 12 divisors, 96 is a largely composite number.^[7]

Skilling's figure, a degenerate uniform polyhedron, has Euler characteristic ${\displaystyle \chi =-96.}$

Every integer greater than 96 may be represented as a sum of distinct super-prime numbers.