This is a common Muslim prostelization technique but it's in error. The word for "day" actually occurs 475 times in the Qur'an and the Islamic calendar is not the same as our generally used solar calendar.
In the Qur'an a month is a lunar month of 29 or 30 days, and the Qur'an explicitly defines the length of a year to be 12 lunar months which is 354 days long, not 365 days.
Why then would Muslims be so eager to prove that the number of occurrences of the word "day" in the Qur'an corresponds to the Western calendar and not to the "divinely mandated" Islamic calendar?
Because many Muhammad apologists engage in lying. Muhammad himself approved of someone lying to further the cause of Islam. Here's one example:
"Muhammad bin Maslama got up saying, "O Allah's Apostle! Would you like that I kill him [Ka'b bin Al-Ashraf]?" The Prophet said, "Yes," Muhammad bin Maslama said, "Then allow me to say a (false) thing (i.e. to deceive Kab). "The Prophet said, "You may say it," (Hadith Vol. 5, Book 59, #369)."
If you point out they are lying, they will then usually change the subject or simply launch another myopic attack like making a case that because the Bible does not condemn something specifically, therefore it is actually advocating its practice (a logical fallacy -
Logic - The Reality and Life Institute); misrepresent some portion of scripture; launch an attack Christian assemblies that have chosen to incorporate; or any of a number of other fallicious tactics. The typical Muslim attack on Christiandom I encouter is always based on lying, twisting scripture to further a false assertion, twisting the facts to misrepresent the truth, and making assertions of fact that are not true.
Because so many Christians in the West are non-intellectual lacking logic, reasoning, and a foundational understanding of Christian apologetics, Muslim proselytizers, as well as all other false religious systems and cults, continue to benefit from lying, misrepresenting history and truth, and engaging in fallicious reasoning.
The 365 Days Hoax
Methods Muslims use to attack Christianity | Christian Apologetics and Research Ministry