The Highest Common Factor of 96m2p5, 32p4 and 8m2n2p3 is:
A. 8p3 B. 4m4n2p12 C. 8p5
To find the highest common factor, we need to factorize each term and find the common factors.
Factorizing the terms:
96m^2p^5 = 2^5 * 3 * m^2 * p^5
32p^4 = 2^5 * p^4
8m^2n^2p^3 = 2^3 * m^2 * n^2 * p^3
Now let's find the common factors:
The common factors of 96m^2p^5 and 32p^4 are 2^5 and p^4.
The common factors of 32p^4 and 8m^2n^2p^3 are 2^3 and p^3.
Therefore, the highest common factor is 2^3 * p^3 = 8p^3.
So the correct answer is A. 8p^3.
To find the highest common factor (HCF) of the given expressions, let's first break down each expression into its prime factors:
96m^2p^5 = 2^5 * 3 * m^2 * p^5
32p^4 = 2^5 * p^4
8m^2n^2p^3 = 2^3 * m^2 * n^2 * p^3
To find the HCF, we need to determine the highest power of each prime factor that appears in all three expressions.
From the prime factorization above, we can see that the highest power of 2 that appears in all three expressions is 2^3, the highest power of m that appears in all three expressions is m^2, the highest power of n that appears in all three expressions is n^2, and the highest power of p that appears in all three expressions is p^3.
Now, let's multiply these highest powers of each prime factor together:
2^3 * m^2 * n^2 * p^3
The HCF is therefore 8m^2n^2p^3 or option B. 4m^4n^2p^12.
So, the answer is option B.