Albert, Bernard and Cheryl again

Logic Level 5

Albert and Bernard know that Cheryl was born in the 1900s. Cheryl tells Albert the number of factors of the number formed by the last 2 digits of her birth year. Then, Cheryl tells Bernard the number of factors of the number obtained by adding 48 to the number formed by the last 2 digits of her birth year.

Albert tells Bernard, "I don't know her birth year."

Bernard tells Albert, "I don't know her birth year."

Albert tells Bernard, "Now I know her birth year."

When is Cheryl's birth year?

Answer in the form $$\text{YYYY}$$.

Details and Assumptions:

If Cheryl's birth year is 1836, then the number formed by the last 2 digits is 36.

Albert and Bernard are perfect at logical thinking.

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