From BiblePortal Wikipedia

Vine's Expository Dictionary of NT Words [1]

1: Χωρίς (Strong'S #5565 — Adverb — choris — kho-rece' )

is used both as an adverb and as a preposition. As an adverb it signifies "separately, by itself,"  John 20:7 , of the napkin which had been around the Lord's head in the tomb; as a preposition (its more frequent use), "apart from, without, separate from." It is rendered "apart from" in the RV of  John 15:5;  Romans 3:21,28;  4:6;  2—Corinthians 12:3;  Hebrews 9:22,28;  11:40;  James 2:18,20,26 . See Beside , Without.

 Matthew 10:29 1—Peter 3:1 4:9

2: Κατά Ἴδιος (Strong'S #2596, #2398 — Preposition — kat' idios — kat-ah' id'-ee-os )

lit., "according to one's own," i.e., privately, alone, is translated "apart" in  Matthew 14:13,23;  17:1,19;  20:17;  Mark 6:31,32 (AV, "privately");   Mark 9:2 .

3: Καταμόνας (Strong'S #2651 — Adjective — kata monas — kat-am-on'-as )

see Alone.

King James Dictionary [2]

AP'ART, adv. a and part See Part.

1. Separately at a distance in a state of separation, as to place.

Jesus departed thence into a desert place apart. Math. 14.

2. In a state of distinction, as to purpose, use or character.

The Lord hath set apart him that is godly for himself.

 Psalms 4 .

3. Distinctly separately as, consider the two propositions apart. 4. Aside in exclusion of as, apart from all regard to his morals, he is not qualified, in other respects, for the office he holds.

Webster's Dictionary [3]

(1): (adv.) Aside; away.

(2): (adv.) Separately, in regard to space or company; in a state of separation as to place; aside.

(3): (adv.) In a state of separation, of exclusion, or of distinction, as to purpose, use, or character, or as a matter of thought; separately; independently; as, consider the two propositions apart.

(4): (adv.) In two or more parts; asunder; to piece; as, to take a piece of machinery apart.

International Standard Bible Encyclopedia [4]

a - part ´ (בּד , badh , "separation," i.e. alone, by oneself; נדּה , nı̄ddāh , "uncleanness" i.e. something put away: "an abomination"): In  Zechariah 12:12-14 the former word is used eleven times with powerful effect to indicate the separation of families and the isolation of wives through excessive grief in Jerusalem on account of the slain Messiah. The latter word signifies removal from ceremonial uncleanness (  Leviticus 15:19;  Leviticus 18:19;  Ezekiel 22:10 ). In Greek, κατ ̓ ιδίαν , kat' idı́an , "by themselves," of marked significance as expressing Christ's desire for privacy in prayer, alone or with His disciples; either in a desert ( Matthew 14:13 ); a mountain ( Matthew 14:23 ); or a high mountain, at the time of the transfiguration ( Matthew 17:1 ,  Matthew 17:19 ), thus suggestive of the secrecy of prayer and communion with God. Used with reference also to Christ's disclosures of His purpose and of the purport of His teaching in private to His disciples ( Matthew 20:17 ).