To reiterate:
• Chinese characters are called hànzì¹
• modern Japanese uses many hànzì, calling them kanji² instead
• katakana³ is used in modern Japanese to write words of foreign origin (loanwords) as well as onomatopoeia and is romanized as katakana, not katagana
• hiragana⁴ is used in modern Japanese to write okurigana⁵, particles, and certain words, and is romanized as hiragana, not hiregana
Here’s a typical (and extremely simple) sentence in modern Japanese that uses all three:
この文はサンプルです。
This is a sample sentence.
この: this (hiragana)
文: sentence (kanji)
は: particle (pronounced wa) (hiragana)
サンプル: sample (loanword; pronounced sanpuru) (katakana)
です: particle (pronounced desu) (hiragana)
――――――
¹ — https://en.wikipedia.org/wiki/Chinese_characters
² — https://en.wikipedia.org/wiki/Kanji
³ — https://en.wikipedia.org/wiki/Katakana
(While we're being pedantic)
です isn't a particle, it's the imperfective (present/future) polite form of the copular verb (to be, in English). The only particle in that sentence is は.
And as a further side note, some words or names normally written in kanji or hiragana are ocassionally written in katakana for emphasis or to emphasize a foreign nature.
[1] In Unicode, they're generally unified into a single set, via process called "Han unification". So, unlike Greek "Α" vs Cyrillic "А", the "same" character that may even look slightly differently in Chinese vs Japanese (e.g. "海"), would have a single codepoint in Unicode. But that's another story...