Other than 1, what are the perfect square factors of 792?
From least to greatest, the perfect square factors
X²_40x+t as a perfect square
To find the perfect square factors of 792, we need to factorize it first.
Let's break down 792 into its prime factors:
792 = 2 * 2 * 2 * 3 * 3 * 11
Now, let's group the prime factors into pairs:
792 = (2 * 2) * (2 * 3) * (3 * 11)
Simplifying each pair of factors:
792 = 4 * 6 * 33
Now, let's break down each factor into its perfect square and non-perfect square components:
4 = 2 * 2 (perfect square)
6 = 2 * 3 (non-perfect square)
33 = 3 * 11 (non-perfect square)
From these factorizations, we can see that the perfect square factor of 792, other than 1, is 2 * 2, which equals 4.
Therefore, the perfect square factor of 792, other than 1, is 4.
To find the perfect square factors of 792, we first need to find the prime factorization of 792. We can start by dividing 792 by the smallest prime number, which is 2.
Dividing 792 by 2 gives us 396.
Dividing 396 by 2 gives us 198.
Dividing 198 by 2 gives us 99.
Now, 99 is not divisible by 2, so let's try the next prime number, which is 3.
Dividing 99 by 3 gives us 33.
Again, 33 is not divisible evenly by 3, so let's try the next prime number, which is 5.
Dividing 33 by 5 leaves a remainder, so let's try the next prime number, which is 7.
Dividing 33 by 7 gives us 4 remainder 5.
Dividing 4 by 2 gives us 2.
Now, we have fully factored 792 into its prime factors: 2^3 * 3^2 * 11.
To find the perfect square factors of 792, we need to look at the exponents of the prime factors. Since we are looking for factors that are perfect squares, we need the exponents to be even.
For 2, the exponent is 3, which is not even.
For 3, the exponent is 2, which is even.
For 11, the exponent is 1, which is not even.
So, the only perfect square factor of 792, other than 1, is 3^2 = 9.
Therefore, the perfect square factors of 792, from least to greatest, are 1 and 9.
792 = 2^3 * 3^2 * 11
so 4 and 9 are the square factors
also 36, of course