كتاب الأشربة
36
The Book of Drinks
(18)
Chapter: It is recommended to lick one's fingers and wipe the bowl, and to eat a piece of food that is dropped after removing any dirt on it. It is disliked to wipe one's hand before licking it, because of the possibility that the blessing of the food may be in that remaining part. The Sunnah is to eat with three fingers
(18)
باب اسْتِحْبَابِ لَعْقِ الأَصَابِعِ وَالْقَصْعَةِ وَأَكْلِ اللُّقْمَةِ السَّاقِطَةِ بَعْدَ مَسْحِ مَا يُصِيبُهَا مِنْ أَذًى وَكَرَاهَةِ مَسْحِ الْيَدِ قَبْلَ لَعْقِهَا

Jabir reported:

I heard Allah's Apostle (ﷺ) as saying: The Satan is present with any one of you in everything he does; he is present even when he eats food; so if any one of you drops a mouthful he should remove away anything filthy on it and eat it and not leave for the devil; and when he finishes (food) he should lick his fingers, for he does not know in what portion of his food the blessing lies.
حَدَّثَنَا عُثْمَانُ بْنُ أَبِي شَيْبَةَ، حَدَّثَنَا جَرِيرٌ، عَنِ الأَعْمَشِ، عَنْ أَبِي سُفْيَانَ، عَنْ جَابِرٍ، قَالَ سَمِعْتُ النَّبِيَّ صلى الله عليه وسلم يَقُولُ ‏ "‏ إِنَّ الشَّيْطَانَ يَحْضُرُ أَحَدَكُمْ عِنْدَ كُلِّ شَىْءٍ مِنْ شَأْنِهِ حَتَّى يَحْضُرَهُ عِنْدَ طَعَامِهِ فَإِذَا سَقَطَتْ مِنْ أَحَدِكُمُ اللُّقْمَةُ فَلْيُمِطْ مَا كَانَ بِهَا مِنْ أَذًى ثُمَّ لْيَأْكُلْهَا وَلاَ يَدَعْهَا لِلشَّيْطَانِ فَإِذَا فَرَغَ فَلْيَلْعَقْ أَصَابِعَهُ فَإِنَّهُ لاَ يَدْرِي فِي أَىِّ طَعَامِهِ تَكُونُ الْبَرَكَةُ ‏"‏ ‏.‏
Reference : Sahih Muslim 2033 d
In-book reference : Book 36, Hadith 177
USC-MSA web (English) reference : Book 23, Hadith 5046
  (deprecated numbering scheme)