Question

Well happy New Year everyone. I've been thinking about the upcoming year "2021" and found something interesting. Reduced to its prime factors it becomes 43*47. Yes, it resolves into 2 CONSECUTIVE 2 digit prime numbers, which does NOT happen that often. The last time this occurred was in 1927 (41 * 47). However these are NOT consecutive prime numbers. (There's another prime number between 41 and 47). If we go back to 1763 (41 * 43), it resolves into two 2-digit CONSECUTIVE primes AND they are TWIN primes (prime numbers with a difference of 2).

And now, here's the question: Can anyone find some interesting factorizations of upcoming years? For example, the year 2033 = 19*107 and the year 2041 = 13*157. In each case the factors are less than 10. Obviously, this is not THE most vital question, so don't spend too much time on it. (Although I've been told that a solution will finally bring about World Peace!!! ) LOL

Answer 1

As 2021 and 1927 does not have any product of primes

HCF and LCM of 2020 and 1926 is shown below

Explanation:

2020 = 2^2 × 5 × 101

1926 = 2 x 3^2 x 107

2 is the HCF

2 x 2 x 3 x 3 x 5 x 101 x 107 = 1945260

1945260 is the LCM

2022 and 1928 both have product of primes and their HCF and LCM is

1949208 is the LCF and 2 is the HCF

1949208 - 1945260 = 3948

3948/2 = 1974

2022-1928 = 94

2020 - 1926 = 94

1974/94 = 21

and brings us back to our year again.

Happy New Year to you.