Here is a solution with only CSS:
.embed-container {
position: relative;
padding-bottom: 56.25%; /* 16x9 */
height: 0;
overflow: hidden;
max-width: 100%;
}
.embed-container iframe {
position: absolute;
top: 0;
left: 0;
width: 100%;
height: 100%;
border: 0
}
<div class="embed-container">
<iframe src="https://www.youtube.com/embed/C0DPdy98e4c"></iframe>
</div>