Hum हम is we in Hindi. With ham, we will always have हैं hain (in present tense only).
We are teachers – हम शिक्षक हैं – ham shikshak hain
We are good – हम अच्छे हैं – ham achche hain
We have three equivalents for our in Hindi. हमारा humaaraa, हमारी humaaree, हमारे humaare. Humaaraa used with masculine singular nouns, hamaaree with feminine singular and plural nouns, and hamaare with masculine plural nouns.
This is our dog – यह हमारा कुत्ता है – Yah hamaaraa kutta hai. Here dog/kutta is singular and masculine and so hamaaraa is used.
These are our dogs – ये हमारे कुत्ते हैं – Ye hamaare kutte hain. Here dogs/kutte is plural and masculine and so hamaare is used.
This is our cat – यह हमारी बिल्ली है – Yah hamaaree billee hai. Here cat/billee is singular and feminine and so hamaaree is used.
These are our cats – ये हमारी बिल्लियाँ हैं – Ye hamaaree billiyaan hain. Here cats/billiyaan is feminine and plural and so hamaaree is used.