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The Gregorian Calendar is solar and the Hebrew Calendar is lunisolar.
In the Hebrew calendar, the month of Av is followed by the month of Elul.
1 week = 1 week on the Hebrew calendar. (The Hebrew week is the same length as the week on the Western calendar)
There isn't any festival celebrated along with Christmas as per the Hebrew calendar, since Christmas is not tied to the Hebrew calendar.
(So every year, Christmas falls on a different date on the Hebrew calendar).
The Hebrew calendar is used in Israel, and by Jews all over the world.