Alumni Meeting Mystery Cache

One day of February 2008, a geocacher Ken joined the alumni meeting of the university he graduated from. Ken met his best friend Taro there after a long interval. They had the following conversation:

Ken: "Are you still a teacher now?"

Taro: "Yeah, my junior high is not so far from here.

Ken: "So did you get married and have kids?"

Taro: "I’m married and have 4 kids."

Ken: "4 kids!?!? That’s amazing in this Japanese declining birthrate society!!! How old are they?"

Taro: "Well…" Taro answered slyly, "The product of their ages is 108 and the sum of their ages is the same as the number of the dormitory room where we stayed while at university!"

Ken: "Huh-uh…that terrible dormi…but I need more information." said Ken after thinking for a moment.

Taro: "The youngest is a boy." added Taro with grin.

Then, wise Ken quickly told Taro the exact ages of his children. Can you determine the ages of Taro’s 4 children---a, b, c, d??? (They are arranged in ascending order. “a” is the youngest.) All the information you need is contained in the description.

After that, they raved about Ken’s favorite game “Geocaching”! Taro was quite interested in that, and the next day, they went to hide the new cache in a Taro's relaxation place to commemorate their reunion!

Ken and Taro installed the cache at:
N 35° 42. (a*b*c*20+d*5)
E 139° 46. (b*c*30+b*d*5+a*b*5)

Now let’s go in search of their cache, folks!!!

The cache is NOT at the coordinates inscribed at the top.
It’s in a heavy muggle place. Be careful to pick it up.
The container is a 35mm film case. Please bring a pen!