The largest perfect square that divides 350584416 is 58430736
The number is given as: 350584416
Express the number as the product of its factors
350584416 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 7 x 7 x 13 x 13
Express the numbers as exponents
350584416 = 2^5 * 3^3 * 7^4 * 13^2
Rewrite the product as:
350584416 = 2^4 *2 * 3^2 * 3 * 7^4 * 13^2
Reorder the factors
350584416 = 2^4 * 3^2 * 7^4 * 13^2 * 2 * 3
Express the product as a product of a perfect square
350584416 = (2^2 * 3 * 7^2 * 13)^2 * 2 * 3
Write out the perfect square (k)
k = (2^2 * 3 * 7^2 * 13)^2
Evaluate the product
k = (7644)^2
Evaluate the exponent
k = 58430736
Hence, the largest perfect square that divides 350584416 is 58430736
Read more about perfect squares at:
https://brainly.com/question/16450266
