When does a Woman who was divorced Three Times become Eligible for Her First Husband

Allah said:

﴿فَإِن طَلَّقَهَا﴾

(And if he has divorced her) meaning, the second husband after he had complete sexual relations with her,

﴿فَلاَ جُنَاحَ عَلَيْهِمَآ أَن يَتَرَاجَعَآ﴾

(it is no sin on both of them that they reunite) meaning, the wife and her first husband,

﴿إِن ظَنَّآ أَن يُقِيمَا حُدُودَ اللَّهِ﴾

(provided they feel that they can keep the limits ordained by Allah.) meaning, they live together honorably. Mujahid said, "If they are convinced that the aim behind their marriage is honorable.'' Next, Allah said:

﴿وَتِلْكَ حُدُودُ اللَّهِ﴾

(These are the limits of Allah,) His commandments and legislation,

﴿يُبَيِّنُهَا﴾

(He makes plain)

﴿لِقَوْمٍ يَعْلَمُونَ﴾

(for the people who have knowledge.)

﴿وَإِذَا طَلَّقْتُمُ النِّسَآءَ فَبَلَغْنَ أَجَلَهُنَّ فَأَمْسِكُوهُنَّ بِمَعْرُوفٍ أَوْ سَرِّحُوهُنَّ بِمَعْرُوفٍ وَلاَ تُمْسِكُوهُنَّ ضِرَارًا لِّتَعْتَدُواْ وَمَن يَفْعَلْ ذَلِكَ فَقَدْ ظَلَمَ نَفْسَهُ وَلاَ تَتَّخِذُواْ آيَـتِ اللَّهِ هُزُوًا وَاذْكُرُواْ نِعْمَتَ اللَّهِ عَلَيْكُمْ وَمَآ أَنزَلَ عَلَيْكُم مِّنَ الْكِتَـبِ وَالْحِكْمَةِ يَعِظُكُم بِهِ وَاتَّقُواْ اللَّهَ وَاعْلَمُواْ أَنَّ اللَّهَ بِكُلِّ شَىْءٍ عَلِيمٌ ﴾

(231. And when you have divorced women and they have fulfilled the term of their prescribed period, either take them back on a reasonable basis or set them free on a reasonable basis. But do not take them back to hurt them, and whoever does that, then he has wronged himself. And treat not the verses (Laws) of Allah in jest, but remember Allah's favors on you (i.e., Islam), and that which He has sent down to you of the Book (i.e., the Qur'an) and Al-Hikmah (the Prophet's Sunnah ـ legal ways ـ Islamic jurisprudence) whereby He instructs you. And fear Allah, and know that Allah is All-Aware of everything).