"biggest share" is correct and usable in written English.
It refers to the largest portion, amount, or percentage of something. For example, "Karen holds the biggest share of stocks in the company."
When the association first began compiling the report in 1987, elementary and secondary education made up the biggest share of state spending, and higher education the second-biggest share.
Magyar Telekom was awarded the biggest share.
This was the biggest share sale anywhere since 2000.
Tesoro had its biggest share gain in almost five years.
Transportation accounts for the biggest share of America's carbon footprint.
Heating, cooling and domestic hot water supply represent the biggest share of energy demands in residential buildings.
Currently the majority of main railway lines in Europe are electrified, and electric trains have the biggest share in the entire amount of rail transport.
Petrobras lost its monopoly in 1997 and made the world's biggest share offering in 2010.
The market in services, which represents the biggest share of economic output, is still fragmented.
He also won the biggest share of voters who valued experience over ideological purity.
There was, however, the promise of perhaps the biggest share buyback in American corporate history.
