Difficult Math Problem #72 - Number Theory
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n*2^7*3^2*7^3 should be divisible by 5^2 and3^3.
Then the minimun value of n is 5^2*3=75.
Please comment,
Regards,
PR
Then the minimun value of n is 5^2*3=75.
Please comment,
Regards,
PR
800guy wrote:If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3), what is the smallest possible positive value of n?
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Write down n x (2^5) x (6^2) x (7^3) as
= n x (2^5) x (3^2) x (2^2) x (7^3),
= n x (2^7) x (3^2) x (7^3)
now at a minimum 5^2 and a 3 is missing from this to make it completely divisible by 5^2 x 3^3
Hence answer = 5^2 x 3 = 75
= n x (2^5) x (3^2) x (2^2) x (7^3),
= n x (2^7) x (3^2) x (7^3)
now at a minimum 5^2 and a 3 is missing from this to make it completely divisible by 5^2 x 3^3
Hence answer = 5^2 x 3 = 75