Answer:
   
   Three is extremely significant in Judaism, as the human condition is
   seen as tripartite: mans relationship to himself and the world of his
   mind, mans relationship to others in the quote real world unquote and
   mans relationship with God. According to the Maharal, this is the
   meaning of the three pillars in Avot 1:2--Torah, Avodah (Service of
   God), and Acts of Kindness.
   
   Next, we have R Samson Refaeil Hirsch, who speaks about the messages
   mitzvot convey through symbols. He speaks of the primary colors in the
   following terms:
    1. Red. The most bent by physical matter (in the rainbow). Also, adom
       (red) is similar to adama (earth), representing mans physical
       nature. This is why the red heifer is burnt as a means of ending
       impurity, and the red string turns white on Yom Kippur when
       atonement was gained, etc.
    2. Green. The color of growth and human growth.
    3. Blue. Spirituality. The color of tzitzis, the walls of Herod's
       temple, the color of the sky. Spirituality.
       
   Note the same triad.
   
   Similarly Hirsch's treatement of numbers: 6 days of physical creation,
   the 7th day of rest, and 8--going beyond the natural order. The eight
   strings of tzitzis (the eighth, according to Maimonides, the blue
   one), the eighth day of Shemini Atzeres, why Chanukah had to be eight
   days, etc.
   
   We can do the same with the three do-or-die sins, the three
   forefathers, the three mitzvos of the seder (the lamb, matzah, and
   maror), the three means of gaining atonement (teshuvah, tefillah and
   tzadakah -- repentance, prayer and charity), the three items in the
   fore-room of the Temple--the table of showbread (12, one for each
   tribe), the menorah (representing wisdom and Torah), and the gold
   altar (for a quote pleasing odor before Gd end-quote), etc.
   
   Kabbalists, such as the Vilna Gaon, ties this back to the three
   aspects of the soul discussed in the Zohar: the nefesh, the life-force
   we share in common with animals (do not consume the blood [of the
   animal], for the blood is of the nefesh); the ruach (lit wind), the
   unseen mind which causes change and motion; and the spiritual
   neshamah.