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.
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The longest factor string for 840 is its prime factorization because prime factors can't be broken down any further.
840 = 2 x 2 x 2 x 3 x 5 x 7
103 is already prime, no need for a factorization.
The prime factorization of 122 is: 2 x 61
11 is already prime.