Find the GCF (greatest common factor) of the following terms.
{3xy,15x^2,21x^3y}
To find the greatest common factor (GCF) of the given terms {3xy, 15x^2, 21x^3y}, we need to determine the highest power of each common factor that appears in all three terms.
To find the highest power of x, we look at the exponent that appears in each term. We see that x appears as x^1 in the first term, x^2 in the second term, and x^3 in the third term. Therefore, the highest power of x that appears in all three terms is x^1.
Next, to find the highest power of y, we look at the exponent that appears in each term. We see that y appears as y^1 in the first and third term, and y^0 (which is simply 1) in the second term. Therefore, the highest power of y that appears in all three terms is y^0 = 1.
Lastly, to find the highest power of the prime number (in this case 3) that appears in each term, we look at the coefficient of each term. We see that the prime 3 appears as a coefficient in the first term (3xy), but does not appear as a coefficient in the second (15x^2) or the third term (21x^3y). Therefore, the highest power of 3 that appears in all three terms is 3^1 = 3.
Putting it all together, the GCF of the given terms {3xy, 15x^2, 21x^3y} is x^1 * y^0 * 3^1 = 3x.