Although Quah (Kē 柯/姬姓柯氏) and Chua/Chuah (Cài 蔡/姬姓蔡氏) are two different surnames, they have the same origin. During the Shang dynasty in China (商朝, 1556 to 1046 BC), there were three brothers who were the sons of Jī Dǎn (姬亶 or 古公亶父 or 周太王) whose surname was Jī (姬/姬姓). Jī Dǎn was the leader of the Zhōu tribe (週部落首), located in Shaanxi province.
The eldest and elder brothers among them were Tài Bó (泰伯/姬泰伯) and Zhòng Yōng (仲雍/姬仲雍), who voluntarily left the Zhōu clan (先週) to the control of their youngest brother Jì Lì (季歷/姬季歷) and founded the vassal state of Wu (勾吳/吳國) near present-day Wuxi (無錫) in Jiangsu province (江蘇省). Tài Bó (泰伯) became the first leader (第一任國君) of Wu (勾吳/吳國) but as he had no male heir, his second brother Zhòng Yōng (仲雍) succeeded him as Wu's second leader (第二任國君).
A descendant of Zhòng Yōng (仲雍 by the name of Kē Xiāng (柯相, 6th generation, 7th Wu lord) adopted Kē (柯) as his surname, which was named after Kē hill (柯山), during a meeting of the vassal state lords. Kē Xiāng (柯相) could thus be considered to be the first in the lineage of Zhòng Yōng (仲雍) to adopt Kē (柯) as the surname. Kē Lú (柯盧, 9th generation, 10th Wu lord) also adopted Kē (柯) as his surname in memory of his great-grandfather Kē Xiāng (柯相).
Jī Fā (姬發), one of the grandsons of Jì Lì (季歷/姬季歷), Tài Bó's (泰伯) and Zhòng Yōng's (仲雍) youngest brother, later conquered the Shang dynasty (商朝) and founded the Zhou dynasty (周朝). Jī Fā (姬發) made one of his brothers, Jī Dù (姬度), lord of the vassal of state Cài 蔡 (姬度封蔡國). Jī Dù (姬度) adopted his state's name as his surname, thus founding the Cài clan (蔡氏始祖), also known as Cài Shū Dù (蔡叔度=姬度).
This story of the three Sin Quah Chuah surnames 辛柯蔡 (Xīn=Sin, Kē=Quah, Cài=Chua), which occurred during the period of the Five Dynasties and Ten Kingdoms (五代十國), an era of political upheaval in China from 907 to 960/979 AD, between the fall of the Tang dynasty (唐朝) and the founding of the Northern Song dynasty (北宋朝), is limited to the family of the senior official Cài (蔡大夫後裔) and does not apply to all other lineages of the Quah and Chuah clans from the Zhou dynasty (BC period).The Wu or Goh (吳) surname shares a common lineage with the Quah (柯) and Chua (蔡) surnames through Tài Bó (泰伯) and Zhòng Yōng (仲雍) who had founded the state of Wu (勾吳/吳國). The last king of Wu (勾吳/吳國) was Fūchāi (夫差, 21st generation, 25th Wu lord) who reigned from 495 to 473 BC. In the latter part of his reign, Fūchāi (夫差) was defeated by Goujian (勾踐) of the state of Yue (越國) after several decades of conflict. Following this victory in 473 BC, Wu (勾吳/吳國) was destroyed and Fūchāi (夫差) forced to commit suicide. After the abolition of the state, Fūchāi's (夫差) three surviving sons were exiled. They and their descendants took Wu (吳) as their clan name.