Square root of 553 is less, than 24, so we should only check the division by the numbers less than 24.
553 is not divided by 2, 3, 5, ... But, it is divided by 7, so, it is composite/
i assume you mean "factorization" in which case; prime numbers can be factored into one and themselved when you make a prime factorization usually using a tree of numbers for instance 12= 3*4; 4= 2*2...