In Japan, as a method of representing a number of years, utilizing era in addition to A.D.
The previous era of the current era Heisei was Showa.
Showa 1 is A.D. 1926 and Showa era is until Showa 64 which is A.D. 1989.
Find the number of times of the year which the year of A.D. can be divided by the year of Showa in Showa era.
The previous era of the current era Heisei was Showa.
Showa 1 is A.D. 1926 and Showa era is until Showa 64 which is A.D. 1989.
Find the number of times of the year which the year of A.D. can be divided by the year of Showa in Showa era.
Answer
For example, when Showa is N years, the year of A.D. will be 1925 + N and the difference is always constant at 1925.
When A.D. 1925 + N can be divided by N, 1925 must also be able to be divided by N.
According to 1925 = 5 × 5 × 7 × 11, N should be 1, 5, 7, 11, 25, 35 and 55.
Seven times
Solution
Showa 1 is A.D. 1926 and the difference is 1925.
For example, when Showa is N years, the year of A.D. will be 1925 + N and the difference is always constant at 1925.
When A.D. 1925 + N can be divided by N, 1925 must also be able to be divided by N.
Therefore, N which is the years of Showa is a divisor of 1925.
Moreover, since Showa is until 64, N is 64 or less number.
According to 1925 = 5 × 5 × 7 × 11, N should be 1, 5, 7, 11, 25, 35 and 55.
Thus it is seven times.
