The last digit is not 0 or 5, so 77 is not divisible by 5.
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- Solution: To find the smallest prime factor of 77, we test divisibility by the smallest prime numbers:
- 77 is odd, so it is not divisible by 2.
- Sum of digits of 77 is \( 7 + 7 = 14 \), which is not divisible by 3, so 77 is not divisible by 3.
- Check divisibility by 7: \( 77 \div 7 = 11 \), which is an integer.
- Thus, 77 is divisible by 7, and since 7 is a prime number, it is the smallest prime factor of 77.
- Therefore, the smallest prime factor is \(\boxed{7}\).
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