Problem Solving

I did not quite understand the explanation - so, please don't repeat the solution from the OG.

In a certain game, a large container is filled with red, yellow, green and blue beads worth, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?

A. 5
B. 4
C. 3
D. 2
E. 0

This problem uses number properties

Find the prime factors of 147000 = 2*3*5*7*7*5*2*5*2 = 2^3*3*5^3*7^2
Notice that the prime factors correspond to the points of the Red Yellow, Green and Blue beads
respectively

Red = 7 points; In 147000, we have two 7's
Yellow = 5 points; In 147000, we have three 5's
Green = 3 points; In 147000, we have one 3
Blue = 2 points; In 147000, we have 3 2's

From this we can clearly see that we have removed two 7's or 2 Red beads

This has to do with factors and multiples.

7r + 5y + 3g + 2b = 147,000

We want to find the value of "r", the number of red beads removed.

Let's do a prime factorization of 147,000.

147,000 = 7 x 7 x 5 x 5 x 5 x 3 x 2 x 2 x 2

We have removed two 7's, so the answer is D.