Husband has Factor V Leiden gene mutation, not on meds, and I’ve had 3 miscarriages and one live birth. Cld his factor v have caused the miscarriages?

Factor V Leiden. If the fetus inherits the gene from a Factor V Leiden paternal carrier , the pregnancy is six times more likely to be affected by clotting which can cause miscarriages and other serious placental malfunctions. It is therefore likely that some or all of the miscarriages were caused by your husband's gene mutation. Get early placental gene testing with your next pregnancy to predict occurrence.
Unlikely. Husband's Factor V Leiden, even if transmitted to the fetus/baby is not likely to result in miscarriage. I am sorry for the loss of pregnancies you suffered, but what you described is not unusual. A woman Factor V Leiden may have miscarriages due to her blood clotting more easily and the clots affecting the placenta.