jonatande wrote:

I'm on my way to re-read my manhattan book again. Btw, it's a strong recommendation to re-read like if it was the first time, but that's another topic.

I do not understand how to think when finding fraction to larger values.

This is an example from the book:

Manhattan Number properties guide CH1 problem set #15

I really need some advice on cognitive approach here, since it seems really hard to put this whole together for similar question as listed below.

Q: A skeet shooting competition awards prizes as follows: The first place finisher receives 11 points, the second place receives 2 7 points, the third receives 5 points, and the fourth place finisher receives 2 points. No other prizes are awarded.

John completes the skeet shooting competition several times and receives points every time he competes. If the product of all the points he receives equal 84,700 How many times does he participate in the competition?

You can write factors of any number by breaking it down into smaller numbers progressively.

Say, 84,700 = 847 * 10 * 10 (10s are easy to break out)

= 7*121*10*10 (You need to deal with 847 first. You can see that it is divisible by 7)

= 7*11*11*2*5*2*5 (We know that 11^2 = 121)

Here, you anyway have help since you know that some 2s, 5s, 7s and 11s are multiplied together to give you the big number.

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