The prime factorisation of 253 is:

1. Test the small primes in turn: 253 is odd, so 2 does not divide it. 2. Its digits sum to 10, so 3 does not divide it either, and it does not end in 0 or 5. 3. Dividing by 11 gives 253 / 11 = 23, and 23 is prime. 4. So 253 = 11 x 23. 5. The other options are not even products of two primes: 36, 84 and 19 x 13 = 247 all fail. _Source: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_