840 = 2 x 2 x 2 x 3 x 5 x 7
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The longest factor string for 840 is its prime factorization because prime factors can't be broken down any further.
2 x 2 x 2 x 3 x 5 x 7
Find one factor, divide by it to get the other factor. Continue separating each of the factors into smaller factors, until you only have prime numbers. For example, 840 = 2 x 420. Now continue finding smaller factors for 420.
No, 3x5x4 is not a prime factorization of 60. A prime factorization of 60 would consist of only prime numbers. The prime factorization of 60 is 2x2x3x5.
When all the factors are prime numbers, that's a prime factorization.