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Given, a number as 343. We need to find out the cube root using prime factorization method.

Step 1: Resolve the given number into prime factors, we get

343 = 7 × 7 × 7 × 1

Step 2: Make pairs of equal factors, we get

⇒ (7 × 7 × 7) × 1

Step 3: Choosing one factor out of every pair, we get

⇒7

Hence, 7 is the cube root of the given number 343 using prime factorization method