The prime factorisation of 253 is:
A11 x 23
B7 x 36
C13 x 19
D3 x 84
Answer & Solution
Correct answer: A. 11 x 23
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: NCERT Class 10 Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_
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