If m and n are positive integers such that the greatest common factor of [tex] m^{2} n^{2}[/tex] and [tex] m n^{3}[/tex] is 45, then which of the following could n equal?
(A) 3
(B) 5
(C) 9
(D) 15
(E) 45

Question

25-07-2017
Mathematics

contestada

If m and n are positive integers such that the greatest common factor of [tex] m^{2} n^{2}[/tex] and [tex] m n^{3}[/tex] is 45, then which of the following could n equal?
(A) 3
(B) 5
(C) 9
(D) 15
(E) 45

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eco92 eco92 · Answer 1 · 2017-07-31T11:51:57+02:00

the greatest common factor of [tex] m^{2} n^{2} [/tex] and [tex]m n^{3} [/tex]

is

gcd(m*m*n*n, m*n*n*n) =m*n*n=[tex]m n^{2} [/tex]

what we did, was to see how many m's and how many n's, each expression have, and then pick the smallest of each letter (factor).

the reason is that the common factor, must have enough m's and n's to divide the m's and n's of both expressions

so
[tex]45=m n^{2} [/tex]
also
[tex]45=5*9=5*3^{2}[/tex]

thus, n is equal to 3

Answer: A)3

If m and n are positive integers such that the greatest common factor of [tex] m^{2} n^{2}[/tex] and [tex] m n^{3}[/tex] is 45, then which of the following could n equal? (A) 3 (B) 5 (C) 9 (D) 15 (E) 45

Respuesta :

Otras preguntas

If m and n are positive integers such that the greatest common factor of [tex] m^{2} n^{2}[/tex] and [tex] m n^{3}[/tex] is 45, then which of the following could n equal?
(A) 3
(B) 5
(C) 9
(D) 15
(E) 45