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The first factors are: Speed, weight, and shape of the projectile. Speed will be determined by the powder charge used to drive the bullet, and the length of the barrel.
Elevation angle (the angle at which the barrel points upward) will then increase or decrease the range based on the first three factors. For most firearms the optimal elevation angle is between 30 and 40 degrees for maximum range.
Other lesser factors include the weather (wind, humidity, temperature) and altitude. Even the Coriolis Effect can play a small factor.
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