Numbers 16:1

Korach took. This passage is beautifully expounded by Midrash R’ Tanchuma.

Korach took. He took himself to a different side, to be disassociated from the community and to cast aspersion on the kehunah. This is why Onkelos translates וְאִתְפְּלֵג, he separated himself from the rest of the community in order to maintain the dispute. Similarly, “why does your heart take you?”— (i.e.,) it takes you to separate you from other people. Another interpretation [of] “Korach took”: He won over the heads of the Sanhedrin among them, with flattering words, as it is said, “take Aharon,” “take words with you.”

The son of Yitzhar, the son of Kehos, the son of Levi. But Scripture does not mention, “the son of Yaakov,” since he [Yaakov] implored [God] for compassion on himself that his name be omitted from their dispute, as it is said, “let my honor not be identified with their assembly.” Where is his (Yaakov’s) name mentioned with Korach? At the genealogical identification [of the Levites] at the platform, in Divrei Hayamim, as it is said, “the son of Evyasaf, the son of Korach, the son of Yitzhar, the son of Kehos, the son of Levi, the son of Yisroel.”

But Korach bar Tizhar bar Kehath, bar Levi, with Dathan and Abiram the sons of Eliab, and On bar Peleth, of the Beni-Reuben, took his robe which was all of hyacinth,

“And Korah took” - This matter that was in the wilderness of Sinai, when the firstborns were replaced and the Levites were separated,
For the Israelites thought that Moshe our Leader did it according to his own thought, to give greatness to his brother, and also to the sons of Kehat for they are close to him, and all of the Levites that they are his family.
And the Levites conspired against him because they were given to Aaron and his sons.
Datan and Aviram conspired because the firstborn privilege was removed from Reuven their father and given to Yosef; perhaps they suspected that [Moshe did that] for the sake of Yehoshua his servant [who was from Yosef].
Also Korah was a first born, for thus was written.
>And those Heads of the Congregation (edah) were firstborns and they were bringing the olah offerings.
And the proof for this explanation is the miracle of the staff (Bamidbar 17:16-26) that all of Israel saw that Hashem chose the tribe of Levi in place of the firstborns, and therefore it is written (Bamidbar 17:25) “their mutterings ceased,” for the mutterings were about this.
Also Moshe said that “it is not from my own mind” (Bamidbar 26:28), because they suspected that it was from his own mind that he did it.
And further proof is “Hashem did not send me” - for this task - because all the Israelites already believed in him [in general]. Another total proof is “all the congregation are holy” and this is a hint to the firstborns that they are holy, because it is written (shemot 13:2) “sanctify to Me every first born” and they are the priests (Kohanim) that approach Hashem and they are the essence of the whole congregation.

VAYIKACH KORACH’ (AND KORACH TOOK). “This section is explained in a beautiful way in the Midrash of Rabbi Tanchuma. (Great), indicates, it is the largest homiletical work of the Rabbis of the Talmud. Next in importance is the Midrash Tanchuma on the Five Books of Moses, composed by Rabbi Tanchuma ben Abba, of the fourth century of the Common Era. This Midrash was very popular, and Rashi relies upon it for a great deal of Agadic material, which he often incorporates into his commentary. On the relationship of the Midrash Tanchuma to Midrash Yelamdeinu, see Volume II, Seder Bo, p. 131, Note 196. Vayikach Korach — he betook himself — “and he took”] is not mentioned in the verse, Rashi explains that it is reflexive in meaning, referring to Korach himself: “Korach betook himself to one side etc.” Ramban suggests a number of other possible interpretations. to one side in order to separate himself from the [rest of the] congregation so that he could contend for the priesthood [which Moses had conferred upon Aaron and his sons, and Korach claimed that it belonged to all Israel]. This is [also] Onkelos’ intention in translating [the word vayikach as] v’ithpleig — ‘he separated himself’ from the congregation to persist in his contention. Similarly, Why ‘yikachacha’ thy heart? means: [Why does your heart] ‘carry you away’ to separate yourself from the rest of the people?”. Thus the language of Rashi.
But the opinion of the Midrash [Tanchuma quoted further on] is not in accordance with the Rabbi’s [i.e., Rashi’s] interpretation, and left his tent, setting up his quarters outside the camp in order to gather people together to rally to him in his dispute with Moses. In Ramban’s opinion, however, the Midrash clearly means that Korach’s heart stirred him up to revolt (Mizrachi), but not that he betook himself elsewhere physically. See also my Hebrew commentary, pp. 254-255. for the Rabbis have said there: “The term vayikach always denotes ‘division,’ [and here it means] that his heart took control of him, in a similar manner to that which it says, Why ‘yikachacha’ thy heart?” The verse thus does not mean to say that Korach betook himself [physically] to one side [of the camp]. Similarly, Why ‘yikachacha’ thy heart? does not mean that it [your heart] takes you to one side to separate yourself [physically] from other people. Instead, the meaning of the [interpretation of the] Midrash on [the phrase] …

ויקח קרח, he approached;

בני ראובן, some of the members of that tribe.

ויקח קרח, The arrangement and meaning of the verse is as if it said: "And Korach, Datan and Aviram, and On ben Pelet took two hundred and fifty chiefs of the congregation, and they rose up before Moses, along with men from the Children of Israel." And after that:

ויקח קרח, “Korach betook himself;” according to the opinion of Rabbi Shimon ben Lakish in the Talmud tractate Sanhedrin, folio 109, the above words mean that Korach made a bad bargain by challenging Moses and Aaron. He caused a “bald spot” among the Israelites, his very name meaning: “bald,” devoid of hair where there ought to be hair. An alternate interpretation of the use of the word: ויקח, at the beginning of this portion. The numerical value of the letters in his name i.e. 308, is equivalent to the word שדד, “he destroyed, laid waste;” he did not observe the laws of the Torah.

בן יצהר, “son of Yizthar;” who had illuminated the earth as does the sun at noon;

בן קהת, “who in turn was the son of Kehat;” who had blunted the teeth of those who begat him. (By becoming infected with his grandson’s ambitions, though personally being a bearer of the Holy Ark)

בן לוי, “the son of Levi;” “who made himself a companion to gehinom, hell.” You may ask why the Torah does not also trace him to the founding father of the Jewish nation, to Yaakov? This is answered by a Rabbi Shmuel son of Yitzchok, who says that Yaakov prayed that his name not be associated with such a person as Korach. This is how he understood Genesis 49,6: בקהלם אל תחד כבודי, “let my honour not be associated with their counsel.”

ודתן, “and Datan,” who flouted Jewish law.

ואבירם, “and Aviram,” “who prevented his heart from repenting.”

ואון, “and On,” who spent all his days in mourning.

בן פלת, “son of Peleth,” a son who performed miracles.”

בני ראובן, “of the members of the tribe of Reuven;” a son who was intelligent enough to correctly interpret the meaning of what his eyes beheld.” Seeing that he was from the tribe of Reuven, Yaakov’s firstborn whom his father had deprived of the privileges of the birthright, Korach thought he had reason to join his rebellion.