What is meant by divisibility of ijtihad is the ability to do ijtihad on some issues and not on all issues or some topics not on all topics. The scholars have differed on this issue into two groups. Some believe that a mujtahid must be an all-rounder and not that he will be sound in some areas and not sound in others. While the other group believes a mujtahid must posses the necessary qualifications required by the issue or the topic on which he wants to do ijtihad not that he must be an all rounder.
The second is the correct and favoured opinion as this has been the practice right from the time of the Companions (May Allah be pleased with them all). More so someone may posses all the necessary qualities of an absolute mujtahid yet he may decide to withhold his judgment because the matter at hand is not that clear to him.
Hence we say it is permissible for a scholar to be a mujtahid in particular topic of fiqh for instance business transaction; he would specialize in it to the extent of having encompassing knowledge of it. Whereas when it comes to matters of hajj he may not be that sound though he has some knowledge about it.
Shaikh ai-Islam Ibn Taymiyyah said:
"Ijtihad is not just one thing that is indivisible. Rather a man may be a mujtahid in a field, topic or issue and not in another field, topic or issue. Hence the ijtihad of every one is according to their capability. So whoever looks into a matter which the scholars have disagreed upon and sees some texts which have no opposition- after he had studied them- backing one of the two opinions is between two options:
One: Is either he takes the opinion of the other person because he is the imaam upon whose madh-hab he is. And this is not a shari'I evidence. Rather an ordinary practice which is contradicted by the practice of another person and the following of another madh-hab.
Two: Or he follows the opinion that is preponderate to him based on the texts that point to it.. Then with this he would have agreed with the imam that disagreed with that imam and the texts would also have been free according to him from any opposition when implemented. And this is the good thing. (Majoo' Fatawa Vol.20/2 I3)