# 154 (number)

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Cardinal one hundred fifty-four
Ordinal 154th
(one hundred fifty-fourth)
Factorization 2 × 7 × 11
Divisors 1, 2, 7, 11, 14, 22, 77, 154
Greek numeral ΡΝΔ´
Roman numeral CLIV
Binary 100110102
Ternary 122013
Quaternary 21224
Quinary 11045
Senary 4146
Octal 2328
Duodecimal 10A12
Hexadecimal 9A16
Vigesimal 7E20
Base 36 4A36

154 (one hundred [and] fifty-four) is the natural number following 153 and preceding 155.

## In mathematics

154 is a nonagonal number.[1] Its factorization makes 154 a sphenic number

There is no integer with exactly 154 coprimes below it, making 154 a noncototient, nor is there, in base 10, any integer that added up to its own digits yields 154, making 154 a self number

154 is the sum of the first six factorials, if one starts with ${\displaystyle 0!}$ and assumes that ${\displaystyle 0!=1}$.

With just 17 cuts, a pancake can be cut up into 154 pieces (Lazy caterer's sequence).[2]

The distinct prime factors of 154 add up to 20, and so do the ones of 153, hence the two form a Ruth-Aaron pair. 154! + 1 is a factorial prime.

## In music

• 154 is an album by Wire, named for the number of live gigs Wire had performed at that time[3]

154 is also:

## References

1. ^ "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
2. ^ "Sloane's A000124 : Central polygonal numbers (the Lazy Caterer's sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
3. ^ "154 - Wire". Allmusic. Retrieved 14 February 2013.