Question

Which of the following prime factorizations represents the greatest common factor of 162, 378, and 414?

2 x 3 ^3
2 x 3 ^4 x 7 x 23
2 x 3 ^2 x 7 x 23
2 x 3 ^2

(P.S. What I'm writing here is irrelevant to the question N.12)

Answer 1

2x3^3

Explanation:

Answer 2

The greatest common divisor is:

`2* 3^2`

Explanation:

The greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

162=2×81

=
`2* 3^4`

378=
`2* 3^3* 7`

and 414=
`2* 3^2* 23`

Hence,

The greatest common divisor is:

`2* 3^2`