Fin GCF of each pair 21. \( 24,48 \mathrm{~m} \) 24. \( 32 a, 48 \mathrm{~b} \) 27. \( 36 \mathrm{k}, 144 \mathrm{~km} \)

To find the GCF of 24 and 48, start by listing the factors: the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, while 48's are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The greatest common factor is 24! Next, for \(32a\) and \(48b\), we can break them down into their prime factors: \(32 = 2^5\) and \(48 = 2^4 \cdot 3\). The GCF takes the lowest power of each prime factor, so we have \(2^4\) common, leading to \(16\) as the GCF. Since \(a\) and \(b\) are included, it’s \(16\) times the GCF of the coefficients (\(ab\)). Finally, the GCF of \(36k\) and \(144km\) is calculated by their primes as well: \(36 = 2^2 \cdot 3^2\) and \(144 = 2^4 \cdot 3^2\). Here, we take \(2^2\) and \(3^2\) which gives us \(36\). Additionally, since \(k\) is common in both terms, the GCF is \(36k\).