1. **State the problem:** Determine if 38, 58, and 76 are all multiples of 19. 2. **Recall the definition:** A number $n$ is a multiple of another number $m$ if there exists an integer $k$ such that $n = m \times k$. 3. **Check each number:** - For 38: $$38 \div 19 = 2$$ Since 2 is an integer, 38 is a multiple of 19. - For 58: $$58 \div 19 = \cancel{58} \div \cancel{19} = 3.0526...$$ Since this is not an integer, 58 is not a multiple of 19. - For 76: $$76 \div 19 = 4$$ Since 4 is an integer, 76 is a multiple of 19. 4. **Conclusion:** 38 and 76 are multiples of 19, but 58 is not.