126 (number)

← 125 126 127 →
← 120 121 122 123 124 125 126 127 128 129 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred twenty-six
Ordinal	126th (one hundred and twenty-sixth)
Factorization	2 × 32× 7
Divisors	1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Roman numeral	CXXVI
Binary	11111102
Ternary	112003
Quaternary	13324
Quinary	10015
Senary	3306
Octal	1768
Duodecimal	A612
Hexadecimal	7E16
Vigesimal	6620
Base 36	3I36

126 (one hundred [and] twenty-six) is the natural number following 125 and preceding 127.

As the binomial coefficient ${\displaystyle {\tbinom {9}{4}}}$, 126 is a central binomial coefficient and a pentatope number. It is also a decagonal number and a pentagonal pyramidal number. As 125 + 1 it is σ₃(5), the fifth value of the sum of cubed divisors function, and is a sum of two cubes.

There are exactly 126 crossing points among the diagonals of a regular nonagon, 126 binary strings of length seven that are not repetitions of a shorter string, 126 different semigroups on four elements (up to isomorphism and reversal), and 126 different ways to partition a decagon into even polygons by diagonals. There are exactly 126 positive integers that are not solutions of the equation

where a, b, c, and d must themselves all be positive integers.

It is the fifth Granville number, and the third such not to be a perfect number. Also, it is known to be the smallest Granville number with three distinct prime factors, and perhaps the only such Granville number.

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