168
168 is the number of hours in a week: 7 × 24.
- Even
- Composite
Where 168 fits
Why 168 is special
168 is the budget everyone actually has. It is the arithmetic of the week — seven days of twenty-four hours — and it is the unit that time-use surveys, shift rotas and working-time regulations are built on, because the week rather than the day is the cycle most work repeats over.
Same number, different meanings
How 168 is understood across different contexts — never implying one meaning because of another.
- Mathematics
168 is the budget everyone actually has. It is the arithmetic of the week — seven days of twenty-four hours — and it is the unit that time-use surveys, shift rotas and working-time regulations are built on, because the week rather than the day is the cycle most work repeats over.
- Everyday life
Time-use research and working-time law both work in weeks rather than days, because most obligations repeat weekly rather than daily. 168 is the fixed total that framing implies: the EU Working Time Directive's 48-hour average and the widely quoted 'eight hours work, eight hours rest, eight hours what we will' are both claims about how to divide it.
- Science
Time-use research, shift scheduling and working-time law all work in weeks rather than days because most obligations repeat weekly. Diary-based time-use surveys of the kind run by national statistics offices allocate the full 168 hours across activity categories so that the totals must reconcile — a design that catches the systematic over-reporting of work and under-reporting of sleep that arises when people are asked to estimate hours directly.
Factors & digit properties
- Divisors (16)
- 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
- Prime factorisation
- 2^3 × 3 × 7
- Digit sum
- 15
- Digital root
- 6
Representations
- Decimal
- 168
- Scientific notation
- 1.680 × 10^2
Roman numerals
C L X V I I I
Binary
1 0 1 0 1 0 0 0
1 × 128 + 0 × 64 + 1 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 168
Octal
2 5 0
2 × 64 + 5 × 8 + 0 × 1 = 168
Hexadecimal
a 8
a × 16 + 8 × 1 = 168
Read as powers of two: 128 + 32 + 8 = 168.
In historical numeral systems
Egyptian
1 coil of rope, 6 hobbles, 8 strokes
1 × 100 + 6 × 10 + 8 × 1 = 168. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
2 vertical wedges (sixties place), 4 corner wedges + 8 vertical wedges (units place)
2 × 60 + 48 = 168. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
rho, then xi, then eta, marked as a numeral
rho-xi-eta + keraia
rho + xi + eta written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
qof, then samekh, then het
qof-samekh-het
qof (100) + samekh (60) + het (8) = 168, written in descending order.
Maya
1 bar + 3 dots (upper, twenties place) over 1 bar + 3 dots (lower, units place)
8 × 20 + 8 = 168. Places stack vertically with the smallest at the bottom, so the upper group is worth twenty times the lower.
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
Related numbers & connections
168 is 7 x 24 — the week expressed in hours. It is the unit that shift rotas and working-time law are written in, because most obligations repeat weekly rather than daily.
View 24 →Everyday life
Time-use research and working-time law both work in weeks rather than days, because most obligations repeat weekly rather than daily. 168 is the fixed total that framing implies: the EU Working Time Directive's 48-hour average and the widely quoted 'eight hours work, eight hours rest, eight hours what we will' are both claims about how to divide it.
DocumentedEveryday life
Science
Time-use research, shift scheduling and working-time law all work in weeks rather than days because most obligations repeat weekly. Diary-based time-use surveys of the kind run by national statistics offices allocate the full 168 hours across activity categories so that the totals must reconcile — a design that catches the systematic over-reporting of work and under-reporting of sleep that arises when people are asked to estimate hours directly.
DocumentedScience
Mathematics
There are exactly 168 prime numbers below 1,000. The count is one of the standard checkpoints of the prime-counting function π(x), and it is already noticeably below what a naive guess suggests: primes thin out as numbers grow, and the density near 1,000 is about one in seven rather than the one in four found below 10. That thinning is what the prime number theorem describes.
DocumentedMathematics
Common questions
How many hours are in a week?
168 — seven days of twenty-four hours. It is the denominator most working-time law and time-use research uses, because obligations repeat weekly rather than daily. Unrelated but worth knowing: there are also exactly 168 prime numbers below 1,000.
Is 168 a prime number?
No, 168 is not prime.
What are the factors of 168?
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
What is 168 in Roman numerals?
168 in Roman numerals is CLXVIII.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 3 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026