**The Common Denominator** was a quiz show that has aired on Channel 4.
The programme was hosted by Phil Spencer.

Contestants are given two phrases, and must state the single word that links the phrases together. For example, the two phrases could be "Wikipedia" and "The United Kingdom", with the link in this case being "Wales"; Jimbo Wales founded Wikipedia, and Wales is a country in the United Kingdom.

Type: Game Show

Languages: English

Status: Ended

Runtime: 30 minutes

Premier: 2013-02-18

## The Common Denominator - Greatest common divisor - Netflix

In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For example, the gcd of 8 and 12 is 4. The greatest common divisor is also known as the greatest common factor (gcf), highest common factor (hcf), greatest common measure (gcm), or highest common divisor. This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see below).

## The Common Denominator - Binary method - Netflix

For further details see Binary GCD algorithm.

d := 0 while a and b are both even do a := a/2 b := b/2 d := d + 1 while a ≠ b do if a is even then a := a/2 else if b is even then b := b/2 else if a > b then a := (a – b)/2 else b := (b – a)/2 g := a output g, d

Example: (a, b, d) = (48, 18, 0) → (24, 9, 1) → (12, 9, 1) → (6, 9, 1) → (3, 9, 1) → (3, 6, 1) → (3, 3, 1) ; the original gcd is thus 2d = 21 times a= b= 3, that is 6. The Binary GCD algorithm is particularly easy to implement on binary computers. The test for whether a number is divisible by two can be performed by testing the lowest bit in the number. Division by two can be achieved by shifting the input number by one bit. Each step of the algorithm makes at least one such shift. Subtracting two numbers smaller than a and b costs

## The Common Denominator - References - Netflix

- http://www.icsi.berkeley.edu/pubs/techreports/tr-92-041.pdf
- https://www.netflixtvshows.com
- https://books.google.com/books?id=K1hCltk-2RwC&pg=PA142
- http://doi.org/10.1016%2F0022-314X(87)90081-3
- https://books.google.com/books?id=3fIUAQAAMAAJ&pg=PA589
- http://doi.org/10.1016%2F0022-314X(72)90038-8
- http://doi.org/10.1007%2FBF01840374
- http://lccn.loc.gov/77171950
- http://www.integers-ejcnt.org/vol8.html
- http://www.stepanovpapers.com/gcd.pdf
- http://demonstrations.wolfram.com/UnderstandingTheLeastCommonMultipleAndGreatestCommonDivisor/