Exhibit 5.1

Goodwin Procter LLP

620 Eighth Avenue

New York, New York 10018

goodwinlaw.com

+1 212 813 8800

June 30, 2026

Factorial Energy Inc.

805 Middlesex Turnpike

Billerica, MA 01821

Re: Securities Registered under Registration Statement on Form S-1

Ladies and Gentlemen:

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-1 (as amended or supplemented, the “Registration Statement”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of the offering by (i) Factorial Energy Inc., a Delaware corporation (the “Company”), of up to 13,800,000 shares (the “Public Warrant Shares”) of Series A common stock, par value $0.00001 per share (the “Common Stock”), of the Company issuable upon exercise of 13,800,000 warrants to purchase Common Stock (the “Public Warrants”), and (ii) up to 86,441,489 shares (the “Selling Securityholder Shares”) of Common Stock to be sold by the selling securityholders listed in the Registration Statement under “Selling Securityholders” (the “Selling Securityholders”), including (a) 13,293,953 shares (the “Option Shares”) of Common Stock issuable upon exercise of options to purchase Common Stock (“Options”) held by certain of the Selling Securityholders, (b) 4,630,954 shares (the “RSU Shares”) of Common Stock issuable upon vesting and settlement of restricted stock unit awards (“RSUs”) held by certain of the Selling Securityholders, (c) up to 6,800,000 shares (the “Private Warrant Shares,” and together with the Public Warrant Shares, the “Warrant Shares”) of Common Stock issuable upon exercise of 6,800,000 warrants to purchase Common Stock (the “Private Warrants” and together with the Public Warrants, the “Warrants”), and (d) 15,512,744 shares (the “Conversion Shares”) of Common Stock issuable upon conversion of 15,512,744 shares of the Company’s Series B common stock, par value $0.00001 per share (“Series B Common Stock”).

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinions set forth below, on certificates of officers of the Company.

The opinion set forth below is limited to the Delaware General Corporation Law.

Based on the foregoing, we are of the opinion that:

1.The Selling Securityholder Shares, other than the Option Shares, RSU Shares, Private Warrant Shares and Conversion Shares, have been duly authorized and validly issued and are fully paid and nonassessable.

2.Assuming the Warrant Shares issuable upon exercise of the Warrants were issued today in accordance with the terms of the Warrants, they would be duly authorized, validly issued, fully paid and nonassessable.

3.Assuming the Option Shares issuable upon exercise of the Options were issued today in accordance with the terms of the Options, they would be duly authorized, validly issued, fully paid and nonassessable.

4.Assuming the RSU Shares issuable upon vesting and settlement of the RSUs were issued today in accordance with the terms of the RSUs, they would be duly authorized, validly issued, fully paid and nonassessable.

5.Assuming the shares of Series B Common Stock were converted today in accordance with the Company’s certificate of incorporation, the Conversion Shares would be duly authorized, validly issued, fully paid and nonassessable.

This opinion letter and the opinion it contains shall be interpreted in accordance with the Core Opinion Principles as published in 74 Business Lawyer 815 (Summer 2019).

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to the Registration Statement and to the references to our firm under the caption “Legal Matters” in the Registration Statement. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/s/ Goodwin Procter LLP

GOODWIN PROCTER LLP