Yes, Handbrake is the way to go. https://handbrake.fr/

Handbrake is the best legitimate converter available

If the original mkv file has both h.264 video and AVC audio, you'll want to use something that just changes the container instead of re-encoding the video.

FFMPEG will copy the video and audio into a mp4 container using a command like this:

ffmpeg -i input.mkv -c:v copy -c:a copy output.mp4

Select allOpen in new window

Copying the streams into the new container will retain the same quality as the original and take less time than re-encoding it.
http://superuser.com/questions/472420/handbrake-settings-to-convert-mkv-to-mp4-while-retaining-the-original-quality

a legitimate mkv to mp4 converter,
well MKV is divx
mp4 -mpeg4 -Moving Picture Experts Group the owners of the DVD mpeg ie vobs. and Divx
http://en.wikipedia.org/wiki/MPEG-4

I use Divx converter free and works great, Divx is a legitimate program no add ware or spyware.
Download this bundle and it includes the divx player, divx converter and divx web player
http://www.divx.com/
or just install them as a single.
What's in it
http://www.divx.com/en/software/divx
Open the divx converter drag and drop your mkv on select output then click start  on theft ..note the directory it will save to
123 done.

"well MKV is divx."

This isn't true. MKV is just a container format, and can utilize a large number (virtually unlimited) of video codecs.
http://en.wikipedia.org/wiki/Matroska
http://en.wikipedia.org/wiki/Comparison_of_container_formats 

"mp4 -mpeg4 -Moving Picture Experts Group the owners of the DVD mpeg ie vobs. and Divx"
This isn't true either. DiVX is a codec that is MPEG-4 Part 2 compliant, but is developed, and thus "owned" by DiVX Inc.
http://en.wikipedia.org/wiki/DivX

There is also MPEG-4 Part 10, which is used by codecs like h.264 and "DiVX HD". So just because something is in a "MPEG4" codec doesn't mean it's DiVX, and software/devices that claim to be "DiVX" compatible may not be able to play all MPEG4 profiles.

Cheers