How many prophecies from Hebrew Scriptures are fulfilled in Jesus Christ’s earthly life? The number of prophecies from the OT  that are fulfilled in the birth and life of Jesus ranges as high as 456  depending on which group you ask.

Do Jehovah’s Witnesses state the exact number of prophecies they believe are thus fulfilled?
It is not a settled matter because different Christian scholars have different ideas  on OT verses that may or may not be foreshadowings or prophecies about Jesus.
All agree that there are more than enough to establish that Jesus is the foretold Messiah. 

A similar question  was asked in a Watchtower magazine. Part of the answer given explains why nailing down an exact number is difficult 


  Not everyone agrees on what is or is not a Messianic prophecy. In his book The Life and Times of Jesus the Messiah, Alfred Edersheim stated that the ancient rabbinic writings classified 456 passages from the Hebrew Scriptures as Messianic, although many of them do not specifically mention the Messiah. 
  
  A close look at these 456 passages raises questions as to whether some of them are prophetic of Jesus Christ. For example, Edersheim said that the Jews regarded Genesis 8:11 as Messianic. They held that “the olive-leaf, brought by the dove, was taken from the Mount of the Messiah.” The author also mentioned Exodus 12:42. Explaining how the Jews incorrectly understood this text, he wrote: “As Moses came out of the desert, so would the Messiah come out of Rome.” 
  Many scholars and others would undoubtedly find it hard to relate these two texts and erroneous explanations to Jesus Christ.
  
  Even if we restrict our attention to those prophecies that were actually fulfilled in Jesus Christ, we encounter difficulties agreeing on an exact number. Take, for example, Isaiah chapter 53, which contains several prophetic features regarding the Messiah. Isaiah 53:2-7 prophesies: “No stately form does he have . . . He was despised and was avoided by men . . . Our sicknesses were what he himself carried . . . He was being pierced for our transgression . . . He was being brought just like a sheep to the slaughtering.” Should this whole passage in Isaiah chapter 53 be counted as one Messianic prophecy, or should each of these characteristics of the Messiah be viewed as a separate prophecy in its own right?
  
  Consider, too, Isaiah 11:1, which reads: “There must go forth a twig out of the stump of Jesse; and out of his roots a sprout will be fruitful.” In verse 10, this prophecy appears again, with similar wording. Should we count these two verses as two separate prophecies or as one prophecy that is repeated? The conclusions reached on Isaiah chapter 53 and Isaiah chapter 11 would clearly affect the total number of Messianic prophecies.
  Hence, we do well to avoid being specific about the total number of Messianic prophecies in the Hebrew Scriptures.


There are lists of prophecy’s that Christian scholars agree on that are helpful for us to build our confidence that Jesus is the promised one from the OT. One such list is found here