find the greatest common factor and the least common multiple of a and b. write your answers as a product of…

Explanation:

Step1: Find GCF - For each prime factor

For each prime factor in the factorizations of A and B, take the lower - power exponent. For prime factor 2: In A, the exponent is 3; in B, the exponent is 2. So we take $2^{2}$. For prime factor 3: In A, the exponent is 3; in B, the exponent is 1. So we take $3^{1}$. For prime factor 5: In A, the exponent is 2; in B, the exponent is 0. So we take $5^{0}=1$. For prime factor 7: In A, the exponent is 1; in B, the exponent is 1. So we take $7^{1}$. For prime factor 11: In A, the exponent is 2; in B, the exponent is 0. So we take $11^{0}=1$. For prime factor 13: In A, the exponent is 3; in B, the exponent is 1. So we take $13^{1}$.

Step2: Calculate GCF

$GCF(A,B)=2^{2}\cdot3^{1}\cdot5^{0}\cdot7^{1}\cdot11^{0}\cdot13^{1}=2^{2}\cdot3\cdot7\cdot13$.

Step3: Find LCM - For each prime factor

For each prime factor in the factorizations of A and B, take the higher - power exponent. For prime factor 2: In A, the exponent is 3; in B, the exponent is 2. So we take $2^{3}$. For prime factor 3: In A, the exponent is 3; in B, the exponent is 1. So we take $3^{3}$. For prime factor 5: In A, the exponent is 2; in B, the exponent is 0. So we take $5^{2}$. For prime factor 7: In A, the exponent is 1; in B, the exponent is 1. So we take $7^{1}$. For prime factor 11: In A, the exponent is 2; in B, the exponent is 0. So we take $11^{2}$. For prime factor 13: In A, the exponent is 3; in B, the exponent is 1. So we take $13^{3}$.

Step4: Calculate LCM

$LCM(A,B)=2^{3}\cdot3^{3}\cdot5^{2}\cdot7\cdot11^{2}\cdot13^{3}$.

Answer:

$GCF(A,B)=2^{2}\cdot3\cdot7\cdot13$ $LCM(A,B)=2^{3}\cdot3^{3}\cdot5^{2}\cdot7\cdot11^{2}\cdot13^{3}$