The smallest number, which is a perfect square and contains 7936 as a factor is:

Concept: A perfect square has every prime factor's exponent even. To find the smallest perfect square that is also a multiple of a given number N, factorise N into primes, identify any prime whose exponent is odd, and multiply N by that prime (once) to make all exponents even.

Working:

1. Factorise 7936: 7936 = 28 × 311.

2. The exponent of 2 is 8, which is already even.

3. The exponent of 31 is 1, which is odd, so one more factor of 31 is needed to make it even.

4. Multiply 7936 by 31: 7936 × 31 = 246016.

Cross-check: 246016 = 28 × 312 = (24 × 31)2 = 4962, and the square root of 246016 = 496, confirming 246016 is a perfect square; also 246016 ÷ 7936 = 31, confirming 7936 is a factor of it.