Exhibit 2.1

amendMENT

to THE

BUSINESS COMBINATION AGREEMENT

This AMENDMENT (this “Amendment”), dated as of March 26, 2026, to the Business Combination Agreement, dated as of December 17, 2025 (the “Business Combination Agreement”), is by and among Cartesian Growth Corporation III, a Cayman Islands exempted company (“CGC”), Fenway MS, Inc., a Delaware corporation (“Merger Sub”), and Factorial Inc., a Delaware corporation (the “Company”).  Each of CGC, Merger Sub and the Company shall individually be referred to herein as a “Party” and, collectively, the “Parties”. Capitalized terms not otherwise defined in this Amendment have the meanings given such terms in the Business Combination Agreement.

WHEREAS, Section 8.3 of the Business Combination Agreement provides for the amendment of the Business Combination Agreement in accordance with the terms set forth therein; and

WHEREAS, the Parties desire to amend the Business Combination Agreement as set forth below.

NOW, THEREFORE, in consideration of the foregoing and the mutual covenants and agreements herein contained, and intending to be legally bound hereby, the Parties hereby agree as follows:

ARTICLE I

AMENDMENTS TO THE BUSINESS COMBINATION AGREEMENT

1.   The sixth paragraph of the Preamble to the Business Combination Agreement is hereby amended and restated in its entirety to read as follows:

“WHEREAS, at least one day prior to the Domestication, the CGC Shareholder Redemption shall occur.”

2.   The eleventh paragraph of the Preamble to the Business Combination Agreement is hereby amended and restated in its entirety to read as follows:

“WHEREAS, at the Closing, CGC, certain CGC Shareholders, Cantor Fitzgerald & Co. (“Cantor”), and certain stockholders of the Company will enter into an Amended and Restated Registration Rights Agreement, substantially in the form attached hereto as Exhibit C (the “Registration Rights Agreement”), pursuant to which, among other things, the parties will be granted certain registration rights with respect to their respective CGC Shares, in each case, on the terms and subject to the conditions therein;”

3.   The definition of “Ancillary Documents” set forth in Section 1.1 of the Business Combination Agreement is hereby amended and restated in its entirety to read as follows:

““Ancillary Documents” means the (a) Registration Rights Agreement, (b) Sponsor Support Agreement, (c) Investor Stock Purchase Agreements, (d) Stockholder Support Agreements, and (e) each other agreement, document, instrument and/or certificate contemplated by this Agreement executed or to be executed in connection with the transactions contemplated hereby.”

4.   The definition of “Company Convertible Notes” set forth in Section 1.1 of the Business Combination Agreement is hereby amended and restated in its entirety to read as follows:

““Company Convertible Notes” means any convertible note or other equity-linked debt instrument convertible into Equity Securities of the Company or any of its subsidiaries outstanding as of the Merger Effective Time.”

5.   The definition of “Required Transaction Proposals” set forth in Section 1.1 of the Business Combination Agreement is hereby amended and restated in its entirety to read as follows:

““Required Transaction Proposals” means, collectively, the Business Combination Proposal, the Domestication Proposal, the Nasdaq Proposals, the Equity Incentive Plan Proposal and the Required Governing Document Proposals.”

6.   The definition of “Nasdaq Proposal” set forth in Section 1.1 of the Business Combination Agreement is hereby amended and restated in its entirety to read as follows:

““Nasdaq Proposals” has the meaning set forth in Section 5.8.”

7.   The following clause (a) is hereby inserted into Section 2.1 of the Business Combination Agreement, directly following the preamble to such Section, and existing clauses (a) and (b) are hereby re-designated clauses (b) and (c) accordingly:

“(a) Pre-Domestication Actions. Upon the terms and subject to the conditions set forth in this Agreement, at least one day prior to the Domestication the CGC Shareholder Redemption shall occur upon the delivery of instructions by CGC to the Transfer Agent to effectuate the Shareholder Redemption, at which time CGC’s obligation to complete the Shareholder Redemption shall become irrevocable.”

8.   Clause (b)(iii) of Section 5.8 of the Business Combination is hereby amended and restated in its entirety to read as follows:

“the adoption and approval of the issuance of the CGC Shares in connection with the transactions contemplated by this Agreement (the “BCA Stock Issuance Proposal”) and the PIPE Financing (the “PIPE Stock Issuance Proposal”) as required by Nasdaq listing requirements (each such proposal, a “Nasdaq Proposal” and, collectively, the “Nasdaq Proposals”);”

9.   Section 5.21 of the Business Combination Agreement is hereby amended and restated in its entirety to read as follows:

“[Reserved.]”

10.   Section 5.22 of the Business Combination Agreement is hereby amended and restated in its entirety to read as follows:

“[Reserved.]”

ARTICLE II

MISCELLANEOUS

1.   No Further Amendment. Except as expressly amended hereby, the Business Combination Agreement is in all respects ratified and confirmed and all the terms, conditions, and provisions thereof shall remain in full force and effect. This Amendment is limited precisely as written and shall not be deemed to be an amendment to any other term or condition of the Business Combination Agreement or any of the documents referred to therein.

2.   Effect of Amendment. This Amendment shall form a part of the Business Combination Agreement for all purposes, and each party thereto and hereto shall be bound hereby. From and after the execution of this Amendment by the Parties, any reference to the Business Combination Agreement shall be deemed a reference to the Business Combination Agreement as amended hereby.

3.   Governing Law. This Amendment shall be governed by, and construed in accordance with, the Laws of the State of New York applicable to contracts executed in and to be performed in that State. Any Action arising out of or relating to this Amendment shall, to the fullest extent permitted by applicable Law, be heard and determined exclusively in any New York State court or Federal court of the United States of America sitting in New York City in the Borough of Manhattan.

4.   Severability. If any term or other provision of this Amendment is invalid, illegal or incapable of being enforced by any rule of law, or public policy, all other conditions and provisions of this Amendment shall nevertheless remain in full force and effect so long as the economic or legal substance of the transactions contemplated hereby is not affected in any manner materially adverse to any Party.

5.   Counterparts. This Amendment may be executed and delivered (including by facsimile or portable document format (pdf) transmission) in one or more counterparts, and by the different Parties in separate counterparts, each of which when executed shall be deemed to be an original but all of which taken together shall constitute one and the same agreement.

[Signature Page Follows.]

IN WITNESS WHEREOF, the Parties have caused this Amendment to be executed as of the date first written above by their respective officers thereunto duly authorized.