The HCF for the three sets of algebraic expression is 32b.
<h3>HCF of algebraic expression</h3>
The HCF of an algebraic expression is the highest common factor present in between given two or more numbers or mathematical expression.
we shall derive the HCF of the algebraic expression by first expressing them as products of the their prime factors as follows;
32a × 5b × 4 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × a × b
24a × 6b × 6 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × a × b
48a × 4b × 5 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × b
Then;
32a × 5b × 4 = (2^5) × b× 2 × 2 × 5 × a
24a × 6b × 6 = (2^5) × b × 3 × 3 × a
48a × 4b × 5 = (2^5) × b × 2 × 5
Hence, the HCF = (2^5) × b
HCF = 32 × b
HCF = 32b
Therefore, we can say that the HCF of the given algebraic expressions is 32b.
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