Hello everyone, any idea on how to approach this problem using prime factorization?

The method listed in the solution in Manhattan is to write down all the factors of each number and move further on that. Is there an easier, less time consuming method?

Find GCF , then all the factors of the GCF will be the ans .

To calculate GCF very quickly notice that all numbers contain a 10 (for eg12 x 10 = 120) so we know they already share a 2 and a 5. After that our question look like 12 , 21 ,27 —> quick notice they all share a 3 so GCF = 2 x 5 x 3 =30

Finding factor of 30 = 8 including 1 they say excluding 1 so 7

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I could complete it till finding the GCF but it didn’t strike me to find the number of factors of the GCF, which was the key. Anyway, thanks for explaining!

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