448
K. 448 is the sonata used in the Mozart effect studies.
- Even
- Composite
Where 448 fits
Why 448 is special
The 1993 paper reported a brief spatial reasoning improvement, and the popular reading — that Mozart makes children cleverer — is not what it found.
Factors & digit properties
- Divisors (14)
- 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448
- Prime factorisation
- 2^6 × 7
- Digit sum
- 16
- Digital root
- 7
Representations
- Decimal
- 448
- Scientific notation
- 4.480 × 10^2
Roman numerals
C D X L V I I I
CDXLVIII uses the subtractive pair XL: ten before fifty — fifty minus ten.
Binary
1 1 1 0 0 0 0 0 0
1 × 256 + 1 × 128 + 1 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 448
Octal
7 0 0
7 × 64 + 0 × 8 + 0 × 1 = 448
Hexadecimal
1 c 0
1 × 256 + c × 16 + 0 × 1 = 448
Read as powers of two: 256 + 128 + 64 = 448.
In historical numeral systems
Egyptian
4 coils of rope, 4 hobbles, 8 strokes
4 × 100 + 4 × 10 + 8 × 1 = 448. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
7 vertical wedges (sixties place), 2 corner wedges + 8 vertical wedges (units place)
7 × 60 + 28 = 448. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
upsilon, then mu, then eta, marked as a numeral
upsilon-mu-eta + keraia
upsilon + mu + eta written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
tav, then mem, then het
tav-mem-het
tav (400) + mem (40) + het (8) = 448, written in descending order.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Abundant number
- Harshad (Niven) number
Related numbers & connections
One work's fame rests on a study whose finding does not match the popular claim.
View 525 →Other connections
- is associated with525
why?
Strength 0.50, confidence "high".
Media & popular culture
K. 448 is the sonata for two pianos used in the 1993 Rauscher study reporting a short-lived improvement in spatial-temporal task performance in adults. Broader claims about intelligence are not supported by that work.
DocumentedMedia & popular cultureGeography: AustriaPeriod: 1781
Common questions
Is 448 a prime number?
No, 448 is not prime.
What are the factors of 448?
The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448.
What is 448 in Roman numerals?
448 in Roman numerals is CDXLVIII. XL is subtractive: ten before fifty — fifty minus ten. Written additively it would be CCCCXXXXVIII, which Roman inscriptions used freely — the strict subtractive form is a later convention.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 15 July 2026