In the Vayu Purana [60.16–18] Suta Gosvami explains:
itihasa-purananam vaktaram samyag eva hi mam caiva pratijagraha bhagavan ishvarah prabhuh eka asid yajur-vedas tam caturdha vyakalpayat caturhotram abhut tasmims tena yajnam akalpayat adhvaryavam yajurbhis tu rigbhir hotram tathaiva ca audgatram samabhish caiva brahmatvam capy atharvabhih
“Shrila Vyasadeva, the almighty Supreme Lord, accepted me [Suta Gosvami] as the qualified speaker of the Itihasas and Puranas. In the beginning there was only one Veda, the Yajur Veda, which Shrila Vyasa divided into four parts. These gave rise to the four activities called catur-hotra, by means of which Shrila Vyasa arranged for the performance of sacrifice. The adhvaryu priests carry out their responsibilities with yajur-mantras, the hota priests with rig-mantras, the udgata priests with sama-mantras, and the brahma priests with atharva-mantras.”
According to Vishnu Purana[3.3.9–10]:
ashöavimshati kritva vai/ veda vyasta maharshibhih vaivasvate 'ntare hy asmin/ dvapareshu punah punah veda-vyasa vyatita ye/ ashöavimshati sattama caturdha yaih krito vedo/ dvapareshu punah punah
"During this period of Vaivasvata Manu's reign, already twenty eight different exalted sages have edited the Vedas in one Dvapara age after another. Twenty eight Veda-vyasas have already come and gone, O best of souls, dividing the Veda into four parts in each Dvapara-yuga"
Vayaviya Samhita of Shiva purana states[7.1.1.37–38]:
sankshipya caturo vedamsh caturdha vyabhajat prabhuh vyasta-vedataya khyato veda-vyasa iti smritah puranam api sankshiptam catur-laksha-pramanatah adyapy amartya-loke tu shata-koöi-pravistaram
“The ingenious Lord abridged the Veda and then divided it [vyasta] into four. Therefore He became known as Veda-vyasa. He also summarized the Puranas in four hundred thousand verses, but in the heavenly planets they still comprise one billion verses”
Shri Vishnu Purana states [3.4.2.–5]
tato ’tra mat-suto vyasa ashöavimshatime ’ntare vedam ekam catush-padam caturdha vyabhajat prabhuh yathatra tena vai vyasta veda-vyasena dhi-mata vedas tatha samastais tair vyasair anyais tatha maya tad anenaiva vyasanam shakha-bhedan dvijottama catur-yugeshu racitan samasteshv avadharaya krishna-dvaipayanam vyasam viddhi narayanam prabhum ko ’nyo hi bhuvi maitreya mahabharata-krid bhavet
"Thereafter, during the twenty-eighth manv-antara, the Lord in the form of my son Vyasa took the one Veda, consisting of four sections, and divided it into four separate parts. Just as this intelligent Vyasa divided the Veda, previously all other Vyasas, including myself, also divided it. O best of the twice-born, understand that in every cycle of four yugas Vyasas come and arrange the Veda into various branches. But know, O Maitreya, that Shri Krishna-dvaipayana Vyasa is Lord Narayana Himself. Who else in this world could have written the great epic Mahabharata?”
Kurma Purana (52.19–20), Vyasadeva’s followers further divided the four Vedas into 1,130 branches:
eka-vimshati-bhedena rig-vedam kritavan pura shakhanam tu shatenaiva yajur-vedam athakarot sama-vedam sahasrena shakhanam prabibheda sah atharvanam atho vedam bibheda navakena tu
“Formerly the Rig Veda was divided into 21 branches, the Yajur Veda into 100 branches, the Sama Veda into 1,000 branches, and the Atharva Veda into 9 branches.”