Given that X= 2 x 3^2 x 7^3 and Y = 2 x 3^2 x 5, find, in index notation, the largest integer hwich is a facotr of X and y
To find the largest integer that is a factor of X and Y, we need to find the highest power of each prime number that is common to both X and Y.
X = 2 x 3^2 x 7^3
Y = 2 x 3^2 x 5
The prime factorization of X is 2^1 x 3^2 x 7^3.
The prime factorization of Y is 2^1 x 3^2 x 5^1.
To find the highest power of each prime number that is common to both X and Y, we take the minimum exponent for each prime number.
For 2, the minimum exponent is 1.
For 3, the minimum exponent is 2.
For 7, X has a higher exponent of 3, but Y does not have a factor of 7.
Therefore, the largest integer that is a factor of both X and Y is 2^1 x 3^2, which is equal to 18 in index notation.