77
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1001 = 7 x 11 x 13
All numbers except primes themselves can be written as a multiple of two or more primes. So you just need to try dividing the number by prime numbers. Trying 13 gives 1001 = 13*77 = 13*7*11. 13, 7 and 11 are all prime numbers, so you know you have found the unique prime factorization of 1001.
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