Question

Find the greatest common factor of the following monomials 44u⁶ v⁴, 6u³ v⁵.

a) 2u³ v⁴

b) 2u³ v⁵

c) 22u³ v⁴

d) 22u³ v⁵

Answer 1

The greatest common factor of 44u^6 v^4 and 6u^3 v^5 is 2u^3 v^4, found by taking the smallest power of each variable common to both terms and the greatest common divisor of the coefficients.

Step-by-step explanation:

The greatest common factor (GCF) of two monomials 44u6 v4 and 6u3 v5 can be found by comparing the coefficients and the powers of each variable in the monomials.

• First, we find the GCF of the coefficients, which are 44 and 6. The greatest number that divides both 44 and 6 is 2.
• Next, we look at the powers of u. Since we are looking for the greatest common factor, we take the smallest power of u, which is u3.
• Lastly, we examine the powers of v. Again, we take the smallest power, which is v4.

Therefore, the greatest common factor of the given monomials is 2u3 v4, which corresponds to option (a).