51 (number)

51
Cardinal fifty-one
Ordinal 51st
(fifty-first)
Factorization 3 \cdot 17
Divisors 1, 3, 17, 51
Roman numeral LI
Binary 1100112
Octal 638
Duodecimal 4312
Hexadecimal 3316

51 (fifty-one) is the natural number 51 following 50 and preceding 52.

Contents

In mathematics

Fifty-one is the 14th discrete biprime and the 5th in the {3.q} semiprime family having the prime factors (3.17). The aliquot sum of 51 is 21, itself a discrete biprime. 51 is the 4th member of the 11-aliquot tree with the sequence (51, 21, 11, 1, 0).

51 is a pentagonal number as well as a centered pentagonal number (one of the few numbers to be both) and an 18-gonal number and a Perrin number. It is also the 6th Motzkin number, telling the number of ways to draw non-intersecting chords between any six points on a circle's boundary, no matter where the points may be located on the boundary.

Since the greatest prime factor of 512 + 1 = 2602 is 1301, which is clearly more than 51 twice, 51 is a Størmer number.

In science

Astronomy

In sports

In other fields

Fifty-one is:

Historical years

51 A.D., 51 B.C., 1951, 2051, etc.

References

Footnotes